Thread: 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 = x-2 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!

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.

has intersection points . So the integral is . Multiplying this result by the constant density does indeed get you a correct answer.