SOLUTION: Reverse the order of integration of the following integral, then calculate it: <img src="https://i.imgsafe.org/d54d2471df.png">

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Reverse the order of integration of the following integral, then calculate it: <img src="https://i.imgsafe.org/d54d2471df.png">      Log On


   

Question 1041431: Reverse the order of integration of the following integral, then calculate it:

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The region of integration is the right half of the parabolic region (or to the right of the y-axis.)
graph%28+300%2C+200%2C+-2%2C+2%2C+0%2C+4%2C+4-x%5E2+%29

int%28+int+%28%28xe%5E%282y%29%29%2F%284-y%29%2C+dy%2C0%2C4-x%5E2%29%2Cdx%2C0%2C2++%29
=int%28+int+%28%28xe%5E%282y%29%29%2F%284-y%29%2C+dx%2C0%2Csqrt%284-y%29%29%2Cdy%2C0%2C4++%29
(In the inner integral, I integrated wrt x only from 0 to sqrt%284-y%29, as per the region of integration.)
=
=int%28+%28e%5E%282y%29%2F%284-y%29%29%2A%28x%5E2%2F2%290%5Esqrt%284-y%29%2Cdy%2C0%2C4+%29
=%281%2F2%29%2Aint%28+%28e%5E%282y%29%2F%284-y%29%29%2A%284-y%29%2Cdy%2C0%2C4+%29
=%281%2F2%29%2Aint%28+e%5E%282y%29%2Cdy%2C0%2C4+%29
=%281%2F4%29%28e%5E%282y%29%290%5E4
=%281%2F4%29%28e%5E8+-+1%29