Find the volume of the given solid...

[lou_skywalker]

1) under the surface z=xy and above the triangle with vertices (1,1) (4,1) and (1,2)
2) enclosed by the cylinders z=x^2, y=x^2 and the planes z=0, y=4

I'm having a hard time setting up the double integral, can anyone help me out?

 

[tkhunny]

This is not good. Did you plot the points? Did you look at the triangle? Did you create the equations of the three lines? Most of this problem is Algebra I. You WILL have to step it up to get through Calculus.

x = 1
y = 1
y = (-1/3)(x-4)+1

\(\displaystyle \int_{1}^{4}\int_{1}^{(-1/3)(x-4)+1} xy\;dy\;dx\)

 

[BigGlenntheHeavy]

\(\displaystyle 2) \ \int_{-2}^{2}\int_{x^{2}}^{4}x^{2}dydx\)