5

16) Evaluate the integral of the following logarithmic function: [ (Inx)"&xQutstiona73x - 4 y = (Sr+ 6)"17) Usc loganthmic differentiation {0 findDLAA...

Question

16) Evaluate the integral of the following logarithmic function: [ (Inx)"&xQutstiona73x - 4 y = (Sr+ 6)"17) Usc loganthmic differentiation {0 findDLAATGNJulcE

16) Evaluate the integral of the following logarithmic function: [ (Inx)"&x Qutstiona7 3x - 4 y = (Sr+ 6)" 17) Usc loganthmic differentiation {0 find DLAATGN Julc E



Answers

Evaluate the integrals.
\begin{equation}\int_{0}^{\ln 16} e^{x / 4} d x\end{equation}

Okay, So let's step would be writing this integral in a form that we know something of their own. 6.12. So we know that we have, um, each other acts and interacts here. So why don't we let you be who to eat your ex, then, do you? Is equal to Drax, the X And that's what we have in our numerator. So rewriting this, we get the integral of you, or actually, that's you over 36 which is six squared, one issue squared. And now we know that, um, he said that X is Austin Ellen of six. So putting in excess Ellen of six we yet U is equal to e a lot of six, which is equal to six. So we now know that you must be less than six. Okay, I'm now looking at their 6.12 again. We see that this is, um, Equation three. And since you is less than six, we have 1/6 tangents, or Harper goaltending interests of X over six and M plus C

To anti derived this expression. We're going to use integration by parts. And we're going to use the six X as the derivative because we want this eventually to derive down to zero. So if that was, um this part that it would be the derivative, that would be six. The derivative, the sex would be zero. So that leaves us tow anti derive. Basically one over three X would be the other expression. Another way to say that is e to the negative react. And we're going to keep integrating this down to that same term as well, so integral of this instead of the derivative with multiplied by negative three. This would divide by negative three. This would be negative one third b. So the negative three acts and then if we just do that one more time, divide by a factor of negative three that would bump it to a positive on ninth E to the negative three X and then we multiply along the diagonal. So these two terms, we're going to multiply with a positive factor, and then these two terms we're going to multiply with a negative factor. So let's do that. So it actually both end up negative here. Um, and so six x times negative one third would be negative two x and then e to the negative three x all of that multiplied. And then we have minus six times 1/9 or six nights. That's two thirds. So minus two thirds mhm to the negative three x and plus C. And that is our, um, anti derivative here. The tabular method works extremely well when one of the terms has a derivative that goes all the way down to zero. So that's what we utilized here, and it be the same thing is, you know, you ve minus vb you as well.

So we got eat to the three minus four x dx here. So let's start using substitution. So you is three minus four x and do you over DX his minus four. So do you. Over Negative four is equal to DX. So moving on from there, Or get in a girl of e to the u times do you over Negative for this means we can just factor out negatives for so that's minus 1/4 into girl a fee to the you Do you integral off each of the U is just going to be e to the U So this will become minus 1/4 he to the u plus c. However, we're not done. We need to plug in three minus four X into you. So this becomes 1/4 each of the three minus four x plus c negative here and this is your final answer.

7.1 Problem number 10 We need to integrate e to the three monies for X dx. One of the key things here is just that that e to the three. That's just a constant. So it may help to just think of this is this is e cubed e to the minus four x dx OK, e cubed is just the constant. So this is e cubed times an integral e to the minus for X dx And how do I integrate this? This is going to be e cubed and then e to the minus four extra integrated to get e to the minus four x but you have to divide by negative four plus a constant of integration. So this is just negative 1/4 e cube you to the minus four x plus a constant. Or you could put this back together and just rewrite it as negative 1/4 e to the three minus for X plus constant of integration. Either those is the equivalent answer


Similar Solved Questions

5 answers
4) The following synthetic reaction mimics terpene rearrangement that occurs in some plants Please provide plausible mechanism for this synthetic process.H,soa
4) The following synthetic reaction mimics terpene rearrangement that occurs in some plants Please provide plausible mechanism for this synthetic process. H,soa...
5 answers
Explain how speed of the magnet changes voltage based on Faraday s law equation:Explain the answer you obtained for (f) based on Faraday' s law.Explain how changing polarity of the magnetic field changes the voltage based on Faraday's law.What does the negative sign at the beginning of the Faraday' $ equation represent?
Explain how speed of the magnet changes voltage based on Faraday s law equation: Explain the answer you obtained for (f) based on Faraday' s law. Explain how changing polarity of the magnetic field changes the voltage based on Faraday's law. What does the negative sign at the beginning of ...
5 answers
In what directions is the derivative of f(x,y) = xy y2 at P(9,4) equal to zero? Select the correct choice below and, if necessary; fill in the answer box to complete your choice_u= (Simplify your answer; Use comma to separate answers as needed: Type your answer in terms of and j ) There is no solution.
In what directions is the derivative of f(x,y) = xy y2 at P(9,4) equal to zero? Select the correct choice below and, if necessary; fill in the answer box to complete your choice_ u= (Simplify your answer; Use comma to separate answers as needed: Type your answer in terms of and j ) There is no solu...
5 answers
Question 142 ptsSuppose no calls are currently on hold If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?Question 152 ptsd) Ifno calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?
Question 14 2 pts Suppose no calls are currently on hold If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? Question 15 2 pts d) Ifno calls are currently being processed, what is the probability that the agent can take 3 minutes for ...
5 answers
Solve the trigonometric equation for all values 0 < € <2 cOsV2 = 0Answet;Submlt Nttwcr#ttoinpt ! Oue 0f 6 / probicm Qut ml MJ
Solve the trigonometric equation for all values 0 < € < 2 cOs V2 = 0 Answet; Submlt Nttwcr #ttoinpt ! Oue 0f 6 / probicm Qut ml MJ...
1 answers
A body is moving in simple harmonic motion with position function $s=f(t)(s$ in meters, $t$ in seconds). Find the jerk at time $t$. $$s=\sin t-\cos t$$
A body is moving in simple harmonic motion with position function $s=f(t)(s$ in meters, $t$ in seconds). Find the jerk at time $t$. $$s=\sin t-\cos t$$...
5 answers
What are the different mechanisms for transferring energy to or from a control volume?
What are the different mechanisms for transferring energy to or from a control volume?...
5 answers
Wl 2 IH! f (to) Find tho Ieft and slns IL0U right 2 2 suodtipn 6 using} Pravlous Prablam } 1 1 L Next Problem SIII 1 12 34/33/31/29 0/2 3 07 Zua
Wl 2 IH! f (to) Find tho Ieft and slns IL0U right 2 2 suodtipn 6 using } Pravlous Prablam } 1 1 L Next Problem SIII 1 12 34/33/31/29 0/2 3 0 7 Zua...
5 answers
#S8 points close t0 the edge on top ofa 5O-foot building throws baseball person standing s()=-8/ 320 50 models the ball" $ vertically upward The quadratic function ground, s(t) , in icet; seconds after I"$ becn thrown; hcight above Ihc What is the maximum hcight of thc bascball? seconds docs it take until the ball hits ground? In how many (In part (6). rund = Ofl 4nSWCr nearest tenth)
#S8 points close t0 the edge on top ofa 5O-foot building throws baseball person standing s()=-8/ 320 50 models the ball" $ vertically upward The quadratic function ground, s(t) , in icet; seconds after I"$ becn thrown; hcight above Ihc What is the maximum hcight of thc bascball? seconds do...
5 answers
Find the geometric mean between the two numbers.$$2 ext { and } 18$$
Find the geometric mean between the two numbers. $$2 \text { and } 18$$...
5 answers
Maria is riding a 30mm diameter Ferris wheel that is making 5revolutions per minute. What is Maria's angular velocity?
Maria is riding a 30mm diameter Ferris wheel that is making 5 revolutions per minute. What is Maria's angular velocity?...
5 answers
Calculate the osmotic pressure of a 0.0158 M solution of NaCl in water at 0 Assume the van't Hoff factor; 1,is 1.94 for this solution.Osmotic pressure atm
Calculate the osmotic pressure of a 0.0158 M solution of NaCl in water at 0 Assume the van't Hoff factor; 1,is 1.94 for this solution. Osmotic pressure atm...
5 answers
Solve for the steady-state probabilities for the following Markov chain. 0 2 1 1 0 0 Hi 3 0
Solve for the steady-state probabilities for the following Markov chain. 0 2 1 1 0 0 Hi 3 0...
5 answers
Time left 6.1924|Nine identical wres, each of d ameter d and lengthL are connected In series; The combination has the same resistance a5 single sirilar wire of length butwhose diameterIS;d/30,9none
Time left 6.1924| Nine identical wres, each of d ameter d and lengthL are connected In series; The combination has the same resistance a5 single sirilar wire of length butwhose diameterIS; d/3 0,9 none...

-- 0.018236--