
double integrals!
hi guys, i have a question that im pretty sure im doing right but i keep gettin the wrong answer. it says:
Find mass and Center of Mass for the following:
Dis bounded by the parabola x = y^2 and the line y = x  2 with density(x,y) = 3. for the mass, i did:
m = (integral from x = 0 to x = 4)(integral from y = x2 to y = x^(1/2) of 3 dydx
I am getting m = 16, but my book says m = 27/2 = 13.5
Could you help me find out what my mistake is??? Thank you in advance!

Bounds of integration
First, you have the wrong bounds of integration. Second, you are integrating with respect to x instead of y. Try drawing the two graphs on a piece of paper and look carefully at the situation.
$\displaystyle x_1=y^2, x_2=y+2$ has intersection points $\displaystyle (1,1),(2,4)$. So the integral is $\displaystyle A=\int_{1}^2 y+2y^2 dy$. Multiplying this result by the constant density $\displaystyle \rho=3$ does indeed get you a correct answer.