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## Homework Statement

Evaluate the triple integral of (x+5y)dV where E is bounded by the parabolic cylinder y=3x^2 and the planes z=9x, y=18x and z=0.

## Homework Equations

## The Attempt at a Solution

My solution is this...

27*6^5 /5 - 162*6^4 /4 + (45/2)*(9*6^6 /6 - 324*6^4 /4) = -797817.6

My steps are here:

Bounds:

0<= z<=9x

18x<= y <=3x^2

0<= x<=6

(x+5y)dzdydx

(x+5y)z

(9yx^2 + 45y^2x /2)dx

[27x^4 - 162x^3 + (45/2)*(9x^5 - 324x^3)]dx

EVALUATED FROM 0 TO 6

27x^5 /5 - 162x^4 /4 + (45/2)*(9x^6 /6 - 324x^4 /4)