5

Evaluate the definite integral using integration by parts:1 x2 e-8x dx f 0(Type your answer correct to 5 decimal places)...

Question

Evaluate the definite integral using integration by parts:1 x2 e-8x dx f 0(Type your answer correct to 5 decimal places)

Evaluate the definite integral using integration by parts: 1 x2 e-8x dx f 0 (Type your answer correct to 5 decimal places)



Answers

Evaluate the integrals by any method. $$ \int_{1}^{5} \frac{d x}{\sqrt{2 x-1}} $$

This all night given problem, Be a team of area but you where you is. Fire X minus one. So we convert a given it tickle internal from few which gives us the Metra's four to nine. True, you do you by five. After solving Dane tickle, we have one by five multiplied by but but you trace 23 and limits us from 4 to 9. Refuting the hair we have won by 52 fruit off nine cubed minus root off for cube which gives us its worn by 52 three cubed minus toe cube Just famous on black five to 27 minus eight Excuse this 19 life.

Okay, This question. We have a soul integration to buy X, d, X and the Limited. Given the question is 125 Okay, so first of all, we will rewrite it. It will be to constant outside the integration and rest will be even by X d x. And the limit is 125 Okay, so it will be too. And the integration of one by X dx It is l n x plus e So it will be l N x okay. And we will not put the constant here because we have the definite limits. So it will be 1 to 5. Okay? Or we can say it will be too. And now we will put the values of limits that is five and one. So it will be l N five minus Ln one. Okay, and now to lm five minus Ln one is zero. So it will be zero and our answer will be to l N five. And this can be also written as Ln five square. Okay. A l n x can be written as Ellen X raised to the power A buy. This property to l N five can be written as Ellen. Five square. Okay. Or we can say the integration of two by X DX. With limits 1 to 5, it will be a land. Okay, this l n five square can merit another land 25. So, Ellen, 25 will be final answer. And when you saw it, it is nearly 3.21 Okay. And this will be our final answer. Thank you.

Okay so we're gonna be finding the value of this definite integral Using um integration by substitution And we're gonna let you equal 1 -1. And then do you would be equal to negative X. and also if U. is equal to 1 -1 then we know that X. Is going to be equal to one minus you. And so what we're gonna do is we're gonna plug in um one minus X in. Are you in for one minus X. And one minus U. N. For X. And so this is equal to the integral from 0 to 1. And we also need to multiply by negative one since D. U. Is equal to not negative xnegative The X. So we need to multiply by -1. And then we're gonna have one minus X. Sorry um one -J Squared Times U. to the 5th do you? And so one minus U squared. That's equal to one and then minus two you and plus U. Squared. And then we're multiplying by U. to the 5th to you. So this is equal to U. to the 5th -2. Year to the 6th plus You to the 7th do you? And now this integral becomes pretty straightforward. Um It's just gonna be an anti differentiation. You're involving the power rule for each of these. So I'm gonna have negative one times you. The six divided by six minus To you to the 7th divided by seven and then plus you to the eighth divided by eight. And we're looking from 0 to 1 however we want to plug in but U. Is equal to so you here is equal to one minus X. So this is equal to negative one Times one -X. to the six divided by 6 -2 times 1 -1. Um To the seventh Divided by seven. And then plus when minus X. To the 8th divided by eight. And now we're looking from 0 to 1. So when X. Is equal to one, each of these terms is equal to zero since we have this one minus X. Factor. So we're really only looking at when X. Is equal to zero. And so when X is equal to zero we get one to the sixth that there's 1/6 and then minus two to the earth two times 1 to the 7th um divided by seven. So really what we're gonna get since we also have this negative sign so we're gonna get zero minus a negative sinus plus sona plus um 1/6 minus 2/7 and plus 1/8. And so what we want to do is get this into a common denominator if we can um or we can just go ahead and plug this into a calculator. I think I'm actually just gonna plug this into a calculator really quickly, So we have 1/6 um and we have minus two divided by seven and plus one divided by eight, And so that is equal 2.00595.

Again. This question. We have to solve integration. Two X minus one DX. And the limit is 25 Okay, so lower, limited to an upper limit is five. So, first of all, we will solve the integration part here, and then we will apply the limits. Okay, So the integration of two x dx will be two x squared by two minus x. Okay. And now the limits it is to is lower limit and five years apart limit. And now we will apply the limits. Their first of all. This, too, will be cancelled by this, too. And it will be X squared minus X. And the limit is 2 to 5. Okay. And now upper limit minus lower limits. So x squared minus x. So it will be five square minus five. That is upper limit. Okay. And now for lower limit, it will be to Squire minus two. Okay, So to solve this, it will be 25 minus five. Okay. And here, four minus two. Or we can say this will be 20 minus. This will be too. So it will be 18, so we can say integration of two X minus one. BX with limits 2 to 5 and there will be 18. And this will be our final answer. Thank you.


Similar Solved Questions

5 answers
Xbock L estions 7Q1 [3/3] Q2 (0/11 Q 3 [5/5] 040MI Q5 (0f11What quaner has the Inreed nicad ot dala? Third QuattetTDiJ [3/3] Q 11 [3/3] [2.5/3] Q 13 (0/21 Grade: 16.5/33 YtvonFirst Quancr Second QuarcrFounk Quartct Whii that sprcad? Find thc Intcr Quartilc Hangc (IQR): Which inicrval has Ihc most data In in?What value could represent dhe S6th pcrcentilc?Get help:Exmple MacBaok AirI 2 73
xbock L estions 7Q1 [3/3] Q2 (0/11 Q 3 [5/5] 040MI Q5 (0f11 What quaner has the Inreed nicad ot dala? Third Quattet TDiJ [3/3] Q 11 [3/3] [2.5/3] Q 13 (0/21 Grade: 16.5/33 Ytvon First Quancr Second Quarcr Founk Quartct Whii that sprcad? Find thc Intcr Quartilc Hangc (IQR): Which inicrval has Ihc mo...
5 answers
Let L : R" 1 R" be a linear isomorphism and f(x) = L(x) + g(x), where Ilg(x)Il < MIlxll? and f is C! Show that f is locally invertible near 0.4.
Let L : R" 1 R" be a linear isomorphism and f(x) = L(x) + g(x), where Ilg(x)Il < MIlxll? and f is C! Show that f is locally invertible near 0. 4....
5 answers
Uing purentheses around ximilar groups. Click in the Simplify the folloning condensed structure by anaker box to #ctivute the palette: CHzOH CH; CHa HOCH? CH;CH CHz-€-CHz-€ CH3 CH, CH;
uing purentheses around ximilar groups. Click in the Simplify the folloning condensed structure by anaker box to #ctivute the palette: CHzOH CH; CHa HOCH? CH;CH CHz-€-CHz-€ CH3 CH, CH;...
5 answers
(1 point) (aj Detenlne the Fourier slne series tor tne functlon fr) x" delned Tor = <x<2jr) 2 si 7where b u16) Delemine Ine Fourier cosine series tor the function g(x) =deilned ior <r<2B(x)Oxcos(nr)where a and %
(1 point) (aj Detenlne the Fourier slne series tor tne functlon fr) x" delned Tor = <x<2 jr) 2 si 7 where b u 16) Delemine Ine Fourier cosine series tor the function g(x) = deilned ior <r<2 B(x) Oxcos(nr) where a and %...
5 answers
Calculate M6 for f(z) = 6 ln(22_ over [1,2]-M64.6355
Calculate M6 for f(z) = 6 ln(22_ over [1,2]- M6 4.6355...
5 answers
If $y=f(x)=frac{a e^{x}+b e^{-x}}{c e^{x}+d e^{-x}}$ is an increasing function of $x$, then find $a$ relation in $a, b, c$ and $d$.
If $y=f(x)=frac{a e^{x}+b e^{-x}}{c e^{x}+d e^{-x}}$ is an increasing function of $x$, then find $a$ relation in $a, b, c$ and $d$....
5 answers
Gaseous butane react wlth gaseous oxygen (02) produce gaseous carbon dioxlde (CO_) and gaseous water (Hzo): (CH,(CH;),CH,) Suppose of butane mixed with 6.4 oxvgen. Calculate the maximum mass of corbon dloxide that couIJ be produced by tha chemleal reaction Round your answer t0 significant dlalts.D.9
Gaseous butane react wlth gaseous oxygen (02) produce gaseous carbon dioxlde (CO_) and gaseous water (Hzo): (CH,(CH;),CH,) Suppose of butane mixed with 6.4 oxvgen. Calculate the maximum mass of corbon dloxide that couIJ be produced by tha chemleal reaction Round your answer t0 significant dlalts. D....
5 answers
Proteins acquire new functions primarily by means ofa. gene duplication, which frees one copy of a gene fromhaving to perform its original function.b. gene duplication, which provides two copies of a gene that, working together, produce a new protein.$c .$ deletions, which generate new protein shapes.detions, which make proteins nonfunctional, thereby creating new opportunities for other proteins.$e .$ None of the above
Proteins acquire new functions primarily by means of a. gene duplication, which frees one copy of a gene from having to perform its original function. b. gene duplication, which provides two copies of a gene that, working together, produce a new protein. $c .$ deletions, which generate new protein s...
5 answers
Where would radicals come in the order of operations? Explain why.
Where would radicals come in the order of operations? Explain why....
5 answers
Solve the IVPdy x - +y = (zy) 3/2 y (1) = 4 dx
Solve the IVP dy x - +y = (zy) 3/2 y (1) = 4 dx...
5 answers
Two long parallel wires carry unequal currents in the same directions ad are separated by a distance of 20 cm The ratig @f the currents is 3 to 1. The magnitude of the total magnetic field at the midpoint between the wires is 13 pT. What is the value of the larger of the two currents (in A) is:
Two long parallel wires carry unequal currents in the same directions ad are separated by a distance of 20 cm The ratig @f the currents is 3 to 1. The magnitude of the total magnetic field at the midpoint between the wires is 13 pT. What is the value of the larger of the two currents (in A) is:...
5 answers
An image is 4.0 mm to the left of a converging lens with focallength of magnitude 5.0 mm. Where is the object for this image?3.An object is 10 cm in front of a concave spherical mirror witha focal length of magnitude 3.0 cm. Where is the image?
An image is 4.0 mm to the left of a converging lens with focal length of magnitude 5.0 mm. Where is the object for this image? 3.An object is 10 cm in front of a concave spherical mirror with a focal length of magnitude 3.0 cm. Where is the image?...
5 answers
Simplify: x2 _ 20x + 14 TmijWhat is the integer remainder?
Simplify: x2 _ 20x + 14 Tmij What is the integer remainder?...

-- 0.020675--