Tripke integration

[think.ms.tink]

Evaluate the triple integral{E} (x + 4 y) dV where E is bounded by the parabolic cylinder y = 2 x^2 and the planes z = 5 x, y = 2 x, and z = 0.

 

[DrMike]

Evaluate the triple integral{E} (x + 4 y) dV where E is bounded by the parabolic cylinder y = 2 x^2 and the planes z = 5 x, y = 2 x, and z = 0.

Please explain what you've tried so far, and where you are stuck.

 

[think.ms.tink]

setting the limits of integration of 0 to 1, 2x^2 to 2x and 0to 5x of x+4y dz dy dx and for my answer i got (50/4-10)... which was incorrect

 

[galactus]

It appears you have the correct integral. You must have evaluated incorrectly. I get 23/6.

\(\displaystyle \int_{0}^{1}\int_{2x^{2}}^{2x}\int_{0}^{5x}(x+4y)dzdydx=\frac{23}{6}\)