volume triple integral

[mcwang719]

The region D is bounded by the parabolic cylinders y=x^2, between z=0 and z=1-y. write out but do not evaluate 6 different triple integrals that gives the volume of D.

I have completed the problem I was wondering if someone could check my work. Thanks!!!!

1. int(-1 to1) int(x^2 to 1) int(0 to 1-y) dzdydx
2. int(0 to 1) int(-sqrt(y) to sqrt(y)) int (0 to 1-y) dzdxdy
3. int(0 to 1) int(0 to 1-z) int(-sqrt(y) to sqrt(y)) dxdydz
4. int(0 to 1) int(0 to 1-y) int(-sqrt(y) to sqrt(y)) dxdzdy
5. int(0 to 1) int(-sqrt(1-z) to sqrt(1-z)) int(x^2 to 1) dydxdz
6. int(0 to 1) int(0 to 1-x^2) int(x^2 to 1) dydzdx

 

[galactus]

The region D is bounded by the parabolic cylinders y=x^2, between z=0 and z=1-y. write out but do not evaluate 6 different triple integrals that gives the volume of D.

I have completed the problem I was wondering if someone could check my work. Thanks!!!!

1. int(-1 to1) int(x^2 to 1) int(0 to 1-y) dzdydx
2. int(0 to 1) int(-sqrt(y) to sqrt(y)) int (0 to 1-y) dzdxdy
3. int(0 to 1) int(0 to 1-z) int(-sqrt(y) to sqrt(y)) dxdydz
4. int(0 to 1) int(0 to 1-y) int(-sqrt(y) to sqrt(y)) dxdzdy
5. int(0 to 1) int(-sqrt(1-z) to sqrt(1-z)) int(x^2 to 1) dydxdz
I believe this one should be:

\(\displaystyle \H\\\int_{0}^{1}\int_{0}^{\sqrt{1-z}}\int_{x^{2}}^{1}dydxdz\)

Please double check

6. int(0 to 1) int(0 to 1-x^2) int(x^2 to 1) dydzdx

 

[mcwang719]

ok i see. (between z=0 and z=1-y). So the other 5 integrals look fine? thanks!