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Initial-Value Problems Due Sunday, Jun 7, 1.59pM1 EDT @0Fe=Initial-valur problcm QuestionWnat !if 4v(7)27 (Express YoUI answer in the form V f())Sorry; that" $...

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Initial-Value Problems Due Sunday, Jun 7, 1.59pM1 EDT @0Fe=Initial-valur problcm QuestionWnat !if 4v(7)27 (Express YoUI answer in the form V f())Sorry; that" $ incorrect Try again?log( -

initial-Value Problems Due Sunday, Jun 7, 1.59pM1 EDT @0 Fe= Initial-valur problcm Question Wnat !if 4 v(7) 27 (Express YoUI answer in the form V f()) Sorry; that" $ incorrect Try again? log( -



Answers

In Problems $41-46,$ evaluate the given definite integral. $$ \int_{0}^{\pi / 4} \tan y \sec ^{4} y d y $$

In this problem we wish to sketch are and then rewrite the integral with the order of integration reversed where the integral is the interval from 0 to 2. Of the integral from y minus two to minus Y. F Dx Dy This question is challenging our understanding of iterated intervals to solve. We must understand that for such integral is the region of integration is given by a limit of integration. That 02 and one minus two to minus why. And be the differentials. That's dx dy. So if we use these quantities to extract the region are we can then easily reverse the order integration. So our region is from y minus 22 to minus Y. In terms of X. And from zero to the intersection to in terms of why has three to share that are to convert to other balance. We see that we have to take two things in. Do I First we have 02 X plus two And then negative 2-0 and then 0 to 2 minus X as well as 0 to 2. Hence we have two integral. Now for our reverse integration, giving us some integral integral negative 2200 exports to f Dy dx 02 integral zero to minus x. F Dy dx.

So this is the graphing question right here. And we want to find a way to compose the function. Um, such that we get the original graph. So if we look at it in terms of this being the general structure, if we want to find the general structure and make that our F value, then we see the general structure is f of X equals the seeking of X times, the tangent of X and then, um, the inside portion because it's x squared X squared that can become our G of X value. So that way, when the G of X is the inside value plugged into this general structure, we get our original function. And as we see, we can turn this graph blue, and it is the same as the original function.

Mhm. And this problem we wish to sketch the region R and then write the integral with a reverse order of integration but not evaluated. We have integral from 0 to 3 of the interval. From 2 to 6. F. Dx Dy This question is challenging understanding of how to work with Federated integral. Remember that for an iterated integral. The regional integration is given by the limits of integration and differentials. So we can extract from our differentials and our limits of integration our region art which will then use to flip the order of integration. So first during the region are we have bounds in terms of X two, I 2, six And thousands in terms of why zero to the intersection of three. Hence the region shaded in red. So to flip these balance will have to go from first to white and then X. Thus we have balance for Y zero two, x over two and for X 0 to 6 which gives us final iterated internal interval 0 to 6 year interval 02 X over to F Dy. Dx

A. Of B. Equal to 500 time. Into the power 0.7 time T. So in this question we have to find the law ethnic terry video. So here we know that for fine laura ethnic David. You D. Natural law F. Of X. Upon D. X. Equal to during the war Add four eggs upon apple eggs. So now we have reply that property here. And we get the dairy video A. Of T. Upon A. Of T. So here. First of all we have to find the derivative of. For a hefty. Which is 500 time 0.07 dying Into the power 0.07 time T. Now we put that value here and we get 500 times 0.07 Time it to the power 0.07 time T. Upon. Now we have to put the value of a property which is 500 time A. To the power suit point 07 times T. So you can see that we simplify this and we get very, very involved A. Of T upon a. Of T equal to 0.07. So it is our final answer.


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