5

6_ Evaluate the iterated triple integral:JG [email protected]?z: dxdzdy...

Question

6_ Evaluate the iterated triple integral:JG [email protected]?z: dxdzdy

6_ Evaluate the iterated triple integral: JG [email protected]?z: dxdzdy



Answers

Evaluate the integral by making the given substitution. $\int \cos ^{3} \theta \sin \theta d \theta, \quad u=\cos \theta$

In this problem. First time integrating the given value with respect to X, considering via the content so I can write the express and has 0 to 1. He took the power White Cube Access Choir by two 02 y divide, simplifying it further. I cannot evaluate one by two, 0 to 1. Why squad it to the power? Why cube dy now let us take why Cuba is equal to T. Then three wise square dy will become DT going forward and solving it. For that I can write y squared dy is equal to D 80 by three when why is it called to zero? Is equal to zero when y is equal to one he is equal to one cube is equal to one now going forward and simplifying it for the so I can write the expression integration of 0 to 1 Why is required it to the power y cube Divide multiplication one by two on solving it I can ride evaluate one by six Integration of 0 to 1 It is the power t d t on further solving. I can ride evaluate one by six he to the poverty from 0 to 1. On further simplification, I get the value of one by six e to the power one minus e to the power he to the power one minus one, which is equal to one by six. E minus one. This is our final answer.

I can write the given integration edge integration 0 to 1 be because as cube from zero to Esquire Bs simplifying it further I can I've 0 to 1 integration as it squad because as cube minus zero ds on further solving I can write Evaluate you go to one as the square multiplication cause Ask you bs on further going now latest take ask you is equal to you So three years is square ds will become the you so access square D s is equal to one by three Do you now? When I extend to zero, you tend to zero So when ash tends to one, you don't tend to one. Therefore the question can be written edged integration of 0 to 1 cause you BU by three on further solving I can write devaluate one by three integration of 0 to 1 because you d which is equal to one by three multiplication Sign you from 0 to 1 which is equal to one by three Sign one minus zero On further solving I get the value edge one by three Sign one This is our answer

Okay, here we go. Uh, we'll start off since s has been held. Constant. This just become a T co sign s cubed from T equals zero to t equals s squared. Okay. And that becomes s squared. Co sign of this. Killed minus zero. Won't zero co sign as a cue? Yes. OK, so we just have this now. Sierra one s squared co sign of s cubed ts, and we're gonna make use of this form the, um Let's see the integral of co sign of you, d you. It's going to be minus sign of you. And we almost have that here. But are you in this case is yes, that's cubed. So do you would be the three s squared ts. Now we have that, except for the three. So you go ahead and put a three in here and put a 1/3 outfront that fixes it. So now we have this exact form and we can then just go ahead. Integrate will have 1/3 sign that's cubed from 0 to 1. It'll be 1/3 sign of one killed minus a sign of zero killed, which will just be in a sign of 1/3

In doing so, we have people with the I drink, just immigration from four who stakes integration from minus 37 By moving towards the solution big given I've treated Antichrist and very 10 as immigration from 4 to 6. Yes, into integration from my last 3 to 7 day. By using Daytona off few Mini. No solving these indicators. We will get X from limit for 26 and to buy from living my history. Who? Seven. So when this, we will get six miners school into seven minus minus tree. That will be 20. So when will be the final answer for your question. Thank you.


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