how solve this 3D integral

i tried to traw the projection of the top interval in the z-y plane

->

so we have a circle

but the radius changes from x to .

which is not possible because when we scan the ring it goes from the biiger radius to the smaller one.

then i thought to try in anyway ,and i wrote the integral in polar

but i dont know how mathmatickly to change the intervals?

how to solve it in a polar way?

Re: how solve this 3D integral

Can you provide the actual and entire problem statement?

Re: how solve this 3D integral

find the volume enclosed by x=y z=0 and

Re: how solve this 3D integral

I'm not seeing the problem. It looks like you have it. Of course, your life may be way easier if you switch x and y.

Re: how solve this 3D integral

how it whould make it easier

Re: how solve this 3D integral

Quote:

Originally Posted by

**TKHunny** I'm not seeing the problem. It looks like you have it. Of course, your life may be way easier if you switch x and y.

it worked

how to solve

Re: how solve this 3D integral

Complete the square: . Let u= y- 1/2 and that becomes so the further substitution v= (1/2)sin(t) gives . That makes .