5

Jxe dx fx" In(x)dr sin( 2x)dx ) fv' sin(2x)dlx (Hint: You have to integrate by parts twice and then solve for...

Question

Jxe dx fx" In(x)dr sin( 2x)dx ) fv' sin(2x)dlx (Hint: You have to integrate by parts twice and then solve for

Jxe dx fx" In(x)dr sin( 2x)dx ) fv' sin(2x)dlx (Hint: You have to integrate by parts twice and then solve for



Answers

Perform the indicated integrations. $$\int x \cos ^{2} x \sin x d x$$ Hint: Use integration by parts.

In this video, we're going to be evaluating the indefinite integral of sine inverse X squared. To start this off, we're going to be using a U substitution where he was going to be the entire into grand sine inverse X squared than the differential of you will be. First, we take the derivative of the outer function scoring function to get two times sine inverse of X now to power one. Now, as per the chain rule, we multiply this by the derivative of sine inverse X, which is one over the square root of one minus X squared and a DX here. Since we're dealing with a differential when we grab you for the entire into grand, all that's left for Devi is DX, which allows Avi to be equal to X itself. So now our solution takes on the form of U times v here to here. So x sine inverse X squared minus the integral off V times. Do you? This includes a constant of two. So I'm gonna include that on the outside. And now we have the anti derivative off X sine inverse of X divided by the square root of one minus X squared DX. This integral that we have here looks quite complicated. If we're able to evaluate it, that we can substitute in that solution back and the problem will be complete. So let's go to a new panel here where our job is to determine how to evaluate X times sine inverse of X divided by the square root of one minus X squared DX one method method we can take with this particular indefinite a girl is let you be equal to sine inverse of X in the U substitution method. The reason this is effective is because the differential do you would be first a derivative of sine inverse X, which is one over the square root of one minus x squared, then multiply by D X. But notice we have that quantity here and here so we can make that substitution right away. But then we'll have one problem here with our ex that can be corrected since if we take this equation here for the U substitution and evaluate sign you on the left hand side than the right hand side would be sign of sine inverse of X, which cancels leaving Justin X. So we can replace Rx with just a you and this integral becomes anti derivative of X sine inverse of X. But we know now that X is going to be a sign of you. Next we let sine inverse of X be equal to you. And finally this quantity here becomes do you. So we dropped the square root of one minus X squared and DX. So now the integral boils down to Can we evaluate to this indefinite integral. If we can, they will substitute the answer back here it looks like this is definitely doable. Since the method of integration by parts can work for this arrangement, we could let's say you be equal to X, in which case do you is DX and let Devi be equal to sign of you, do you? In which Case V would be equal to negative co sign of you. Let's write this in to this line. We'll have first U times V, which is equal to negative X times co sign of you. Then we take away the integral of the times, do you, which includes a negative sign so we can convert this to positive if we like and we obtain co sign of you times d you So we're now ready to get to the last step of this process and we have that this becomes negative. X Times CO sign of you the anti derivative of co signing you is plus sign of you and will have arbitrary constants C of integration. Finally, if we substitute back in the quantity that you assign inverse effects, this will turn into negative X Times Co sign of sign in verse of X plus. Here we would have sign of sine inverse of X, but that's just a X once again, just like how he obtained that expression plus a constant. Now we're ready to go back to our original solution Over here on the left we have that this becomes X times sign in verse of X squared minus two times the expression that we just found a negative x Times co sign of sine inverse of X plus X close parentheses and at a concert of integration. And this expression here is our solution. If we like, we could distribute negative to inside to obtain X times sine inverse of X squared plus two x times co sign of sine inverse of X minus two x plus a constant. And this is the evaluation for this indefinite integral

We're asked you find the inter troll of sine X lawn of kynect he act and we're gonna do that First of all by using part Let u equal long on a side act because we can't integrate the lot of sign Expert a waste Or do you is one over sign Next times coastline acts. And then, if that's the case, then Devi is gonna be tied at the X Very my pen. Zach, Enough. Your sign. Act the act. And that means that V is co side acts of native. So when we write this, we get you time to be. But my co sign act Lawn of China And then it's plus the integral of VD you It was plus the integral of minus coats. I neck multiplied by co sign over Sinek Okay, DX, This should have a d Exxon. So if I simplify that a little bit, I have minus boot sign act blond outside. And then it's my Inderal of boots. I am spared Act over d efs, which is closed Canada Dia. Now it's it's real here, back to the whole thing. What I'm gonna do is I'm gonna write that at brand is one of words on game time's called Darling Square Day de Act. Then I have a problem because I can't take the role of that. The one word I can't directly. So I'm gonna write posts. I squared, act as one minus over signing. Do yet. Okay. And then give me the interval. Want DX and in might, you know? Yeah. Okay. Now I just splitting one divided by sine accident Science Great. Divided by sine X. Now, if you think about one over sign next, that's Cosi connects this burning like it, right. You get that. If you look in your the inner glow of that is that is a long of teak and acts okay. Minus seats would go back now to the whole thing and writer final answer his finest coats. I necked a lot of sine X. That's our first term there. And then what? Mitt interval or undermining the central. So mine. It's upon my it. What's he? And that is our answer again. If you look back up here, you can kind of follow that through hopefully and see where I'm getting all that from. But that's our answer for this

In this fusion. The given integral is that is integral. Cynics- School six divided by sine X. Dx. So now in the community saying that we have to solve this Cuban integral. So let's start answering this fusion. So first I will I will making the appropriate algebraic transformation. So the given integral is that is Integral sign X- School six divided by syntax will be witness after dividing by cynics with every term of immigrant. So in the new matters of integrated so it will be written as studies integral. Cynics divided by cynics. Okay. D x minus integral cortex divided by sine X. Dx. Here I also apply a unity of integral. So no I can say that the given integral that is integral cynics. Meniscus sex divided by sine X D X is equal to this will become Daddy's Sinus Sinus divided cynics. Will you at least one. So I can see that integral. Dx minus integral. Cossacks divided by cynics. D X. No next step is look the right side of this step. So I can say that this is a shape number one. And uh here in the right side this time will do after taking integration of dX about that should be that is X. And uh for what? No and write the second term of right right side as it is. That is minus integral cortex. Synnex divided by sine X. Dx. So for finding this term I will use a method that is called substitution matter and apply it. And so it means I will my next step is I will find this turn separately by using the substitution method. So I can say that let's assume that U. Is equal to cynics then no Take a differentiation on both sides. So it will be regional status d. U. is equal to cost 60 x. So now I considered I'm giving numbering to both the steps. So I consider this is a step number two and this is step number three. So this term which is sitting on right side In a step # one. So I considered integral core sex. Synnex. Sorry Cosette dx divided by cynics will be written as that is integral by using step number two. And the step number three it will be written us that is do you over you? No, we know the extended integration formula that is integral. You to deport minus one. The U. Is equal to Ellen absolute value of you plus C. So use this formula for finding the integration of one hour. You do you. So I can say that the term that is which is written on right side second term that is integral cause sex the X do I did by cynics is equal to airline. By using this extended integration formula I can say that Ellen absolute value of you plus see now put the value of you by using each tape. Number two that is U. Is equal to sign next. So I will say it. The result will be eaten as it is integral. Cossacks dx divided by sine X is equal to Ellen cenex. Yeah plus C. No, I considered this is a step number four and now this step number put the step number of four in a step number of one. So let me see in this tape. So the given integral will Britain as it is. Yeah integral cynics minus core sex divided by sin X. Dx is equal to x minus. Now put the value of this turn In the step # three. So I can see that X minus Ellen absolute value of cynics minus C or against it. I'm considering this is another time. That is constant time, that is C1. So it means the answer is that is given integral answer is there is x minus Ellen absolute value of cynics. Let's see one. So this is the answer forgiven integral, jettison x minus core sex divided by sine X. Dx. So I had sold the occasion. Thank you.

In discussion. The given integral is X times science squid X. The X. Here we have to solve this integral by using integration by parts. So let u. equals two x phoenix On differentiating it it becomes the U. equals two X times what's next? Let's try next. The X. similarly let TV equals two cynics E X. On integrating both sides, we get equals two minus cosine X. Now we will use the formula for integration by parts. So we can try this integral S X times. Find square X. B X equals two X. As in X multiplied by minus cosine X minus integral of minus cosine X multiplied by expose the next plus cynics the X in simplified form because I do guys minus. Excuse me. Next multiplied by cynics plus integral. Off X times ho Zion square eggs B X. Plus integral of cosine X. Multiplied by cynics the X. No, we can write whole science correct in terms of thanks. Good. X. So minus X times Jose. Next multiplied by cynics plus. Can take it all off X times one minus sine square X E x plus integral of Joseon X. Multiplied by cynics E X. In simplified form we can diet test minus X. Cosine X. Multiplied by cynics plus integral off X. Dx minus integral of X times. Sine squared X. The X plus integral of cosine X. Multiplied by cynics B. X. No baby lad integral of X times Find square X the X to both sides. And let you request to phoenix on differentiating it it becomes. Do you request to go phoenix X? Now we will substitute in this situation. So it becomes food banks integral. X- nine sq X the X. It was two minus X. Co sign X. Multiplied by sign. Next Plus one x 2. X square plus integral. You do You minus X. X times person X multiplied by cynics Plus one x 2. X Square Plus. Integration of this party is given by one x 2. You square. Now we will substitute the value of you here which is the next so it becomes minus X. Cozy. Next multiplied by cynics Plus one way to x square Plus one by to Find Square X. Now we will divide by two on board decides so it becomes integral. Off X times sine squared X. The X equals two -1 x two. Excuse me Next. I want to be played by cynics pressed one x 4 x sq plus But by four science, correct plastic. Thank you.


Similar Solved Questions

5 answers
(15 points) Let f: 2 ~ Ziz be thee function f(r) [rhz: points) List two elemnents in the preimage f-'([5]).(8 points) Describe the preimage f-'([5]) in set notation: f-'(F5]) =
(15 points) Let f: 2 ~ Ziz be thee function f(r) [rhz: points) List two elemnents in the preimage f-'([5]). (8 points) Describe the preimage f-'([5]) in set notation: f-'(F5]) =...
5 answers
2. 0 <r and x < 2 2 <*f(x)
2. 0 <r and x < 2 2 <* f(x)...
5 answers
Ahummingbird is flving around and its velocity rightwards is the positive velocity direction:functian of timagiven In the graph below where(m/s)7t(s) 3.50,5LS2.5What is thc hummingbird $ displacement Az from t 3.0s to 3,5 8?Answer with two significant digits;
Ahummingbird is flving around and its velocity rightwards is the positive velocity direction: functian of tima given In the graph below where (m/s) 7t(s) 3.5 0,5 LS 2.5 What is thc hummingbird $ displacement Az from t 3.0s to 3,5 8? Answer with two significant digits;...
5 answers
QuestionApply the backflow algorithm to the digraph belowTI (5)T9 (I0)T2 (61Ti0 (12)TJ (21Taskcritical tImeTask 2 has critical timeQucstion Help: Qvidco OvideoSubmit Qucstion
Question Apply the backflow algorithm to the digraph below TI (5) T9 (I0) T2 (61 Ti0 (12) TJ (21 Task critical tIme Task 2 has critical time Qucstion Help: Qvidco Ovideo Submit Qucstion...
5 answers
Evaluate the following combination13 10Give your answer as an integer.
Evaluate the following combination 13 10 Give your answer as an integer....
5 answers
1. #ow pm' hle hooLs % 23 a1 thu { mary fetum ~Le pns"hve ^ost $ 23 exp w7 A , E_ eac a4 foe % 67l tthe +~hve
1. #ow pm' hle hooLs % 23 a1 thu { mary fetum ~Le pns"hve ^ost $ 23 exp w7 A , E_ eac a4 foe % 67l tthe +~hve...
5 answers
The traffic flow rate (cars per hour) across an intersection is r(t) 200 + 700t 210t2 , where t is in hours, and t-0 is 6am. How many cars pass through the intersection between 6 am and 9 am?cars
The traffic flow rate (cars per hour) across an intersection is r(t) 200 + 700t 210t2 , where t is in hours, and t-0 is 6am. How many cars pass through the intersection between 6 am and 9 am? cars...
1 answers
Let $S=\left\{x_{7}, x_{6}, \ldots, x_{1}, x_{0}\right\} .$ Determine the 8 -tuples of $0 \mathrm{~s}$ and 1 s corresponding to the following subsets of $S$ : (a) $\left\{x_{5}, x_{4}, x_{3}\right\}$ (b) $\left\{x_{7}, x_{5}, x_{3}, x_{1}\right\}$ (c) $\left\{x_{6}\right\}$
Let $S=\left\{x_{7}, x_{6}, \ldots, x_{1}, x_{0}\right\} .$ Determine the 8 -tuples of $0 \mathrm{~s}$ and 1 s corresponding to the following subsets of $S$ : (a) $\left\{x_{5}, x_{4}, x_{3}\right\}$ (b) $\left\{x_{7}, x_{5}, x_{3}, x_{1}\right\}$ (c) $\left\{x_{6}\right\}$...
5 answers
19. What is the product of the following reaction sequence?CH;CHCHzNHz CH;CHZCCILAIHACH;CH,CH-NCH,CH,CH; OH CH;CH,CHNHCH_CH_CH; B C CH,CH CH NH D. (CH;CH CH:)NH
19. What is the product of the following reaction sequence? CH;CHCHzNHz CH;CHZCCI LAIHA CH;CH,CH-NCH,CH,CH; OH CH;CH,CHNHCH_CH_CH; B C CH,CH CH NH D. (CH;CH CH:)NH...
5 answers
Which high energy intermediate can generate more ATP through the electron transport chain?Neither NADH nor FADH2 are involved in ATP production in electron transport Both NADH ad FADH2 generate the same amount of ATPFADH2NADH
Which high energy intermediate can generate more ATP through the electron transport chain? Neither NADH nor FADH2 are involved in ATP production in electron transport Both NADH ad FADH2 generate the same amount of ATP FADH2 NADH...
5 answers
Solve the given problems involving limits.Draw the graph of a function that is discontinuous at $x=2,$ has a limit of 2 as $x ightarrow 2,$ and has a value of 3 at $x=2$
Solve the given problems involving limits. Draw the graph of a function that is discontinuous at $x=2,$ has a limit of 2 as $x \rightarrow 2,$ and has a value of 3 at $x=2$...
5 answers
6642 44 ochz Thochz LaId (Cs")lBa 05LzPd sn (C1cy N
6642 44 ochz Th ochz LaId (Cs")l Ba 0 5 LzPd sn (C1cy N...
3 answers
Suppose that the lamina Q is the region bounded by the curves y = Vx , Y =1 and the y-axis as shown below.0. 06 X08The variable density of the lamina is given by S(x,y) = 360 x4 y2 . Hence the Mass of the lamina is given by Je S(x,y) dA Given that the mass of the lamina is 72 13 find the centre of mass (x, Y) of the lamina_Enter the exact value of your answers in Maple syntax in the boxes below:
Suppose that the lamina Q is the region bounded by the curves y = Vx , Y =1 and the y-axis as shown below. 0. 06 X 08 The variable density of the lamina is given by S(x,y) = 360 x4 y2 . Hence the Mass of the lamina is given by Je S(x,y) dA Given that the mass of the lamina is 72 13 find the centre o...
5 answers
PobuhionbuclonaglotOiyon Ov #'Qe ni45i nmentIoonl ( (riltnita)Sat Up tho doilnlia Intogunl Inal Onvonchundd(ntanlulu 0 ponuallen ItctnDin e Unltweinht al Ihe populatian from 0 t0 | = 3 /abou Tho chunge Yuntll tha final anewnt_ Thnntoung annimaruethundr (Do not roundnanmmm Iligrat? #qunred mnligrama cubad
pobuhion buclona glot Oiyon Ov #'Qe ni45i nment Ioonl ( (riltnita) Sat Up tho doilnlia Intogunl Inal Onvon chundd (ntanlulu 0 ponuallen Itctn Din e Unlt weinht al Ihe populatian from 0 t0 | = 3 /abou Tho chunge Yuntll tha final anewnt_ Thnntoung annimaruethundr (Do not round nanmm m Iligrat? #q...
5 answers
Find the Consider 2 ? 9 the { glven probabllity 3 Tne Tne card is a card caro /> € experiment of drawing I# (Enter your probability sinaie Caru rundom fractlon ) trom deck 1 Dune 1 Lanlo
Find the Consider 2 ? 9 the { glven probabllity 3 Tne Tne card is a card caro /> € experiment of drawing I# (Enter your probability sinaie Caru rundom fractlon ) trom deck 1 Dune 1 Lanlo...
5 answers
A pencil case contains three blue pens, two red pens; and five pencils. If you reach in and randomly select a writing instrument; what is the probability that it isred pen? blue pen?b)pen?not a
A pencil case contains three blue pens, two red pens; and five pencils. If you reach in and randomly select a writing instrument; what is the probability that it is red pen? blue pen? b) pen? not a...
5 answers
The PTA is forming subcommittee t0 purchase new equipment for the school's hockey team There are thirteen parents and twelve teachers wo are available t0 join this 6-person subcommittee_ In how many ways can the subcommittee be formed if there must be at least teacher on it?
The PTA is forming subcommittee t0 purchase new equipment for the school's hockey team There are thirteen parents and twelve teachers wo are available t0 join this 6-person subcommittee_ In how many ways can the subcommittee be formed if there must be at least teacher on it?...
5 answers
Problem 1. SAVE and PREVIEW ONLY ANSWERS NOT SUBMITTED FOR GRADINGpoint) Determine an antiderivative, Y, of the given derivative, Y Then use the given condition on y to determine the constant of integration.dy 8x -2 + 4x-1 -4; y(1) = 8 dxSAVE and preview answersEntered Answer Preview
Problem 1. SAVE and PREVIEW ONLY ANSWERS NOT SUBMITTED FOR GRADING point) Determine an antiderivative, Y, of the given derivative, Y Then use the given condition on y to determine the constant of integration. dy 8x -2 + 4x-1 -4; y(1) = 8 dx SAVE and preview answers Entered Answer Preview...

-- 0.023370--