Here it is with the variables chosen/labelled slightly different. I also have this
Will link to the thread if I find it.
I've been able to solve parts A, B, and D of this question. But I'm really stuck on Part C. Could someone offer some insight?
Part A:
This follows from integration by parts:
,
,
Part B:
Substitute , . It follows that x=g(y). Then we substitute values into formula from part A, remembering to change the bounds: When x=a, y = f(a). When x=b, y = f(b).
Part c:
Stuck on this.
Part d:
Using formula from Part B, we simply plug in values and find that the integral evaluates to 1.
Thanks,