How Do You Calculate the Triple Integral of (x+5y) in a Bounded Region?

[Larrytsai]

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)

 

[vela]

I refer you to your other thread for the same problem.