Setting Up a Triple Integral for x^2e^y Bounded by z=1-y^2, z=0, x=1, and x=-1

[Yezman]

I've tried every possible way to set this up that I know of and even using mathmatica I can't get the proper answer... Can someone just explain to me how to set it up (once I know the limits I can solve it)

x^2 e^y bounded by

z= 1-y^2
z = 0
x = 1
x = -1

I plan to set it up as a dzdydx

So the outer most limits are fairly easy... -1 and 1... But i am lost and frustrated as to the rest... I tried solving for y, but that didn't get me far. Can someone explain to me how to do this.

Thanks

 

[LCKurtz]

I've tried every possible way to set this up that I know of and even using mathmatica I can't get the proper answer... Can someone just explain to me how to set it up (once I know the limits I can solve it)

x^2 e^y bounded by

z= 1-y^2
z = 0
x = 1
x = -1

I plan to set it up as a dzdydx

So the outer most limits are fairly easy... -1 and 1... But i am lost and frustrated as to the rest... I tried solving for y, but that didn't get me far. Can someone explain to me how to do this.

Thanks

The first step in setting it up is to draw a picture. Have you done that?

Once you have the picture, think of a little dzdydx element out in the middle of the solid. z goes from z on the lower surface to z on the upper surface. Then you look in the xy plane for the y and x limits.

 

[schaefera]

Well, the limits in the xy-plane are x=+/- 1 which is given, but then z=0 when 0=1-y^2, so y^2=1, y=+/-1 as well... so the outer two limits go from -1 to 1 and the dz limit goes from 0 to 1-y^2.