# double integrals!

• Oct 29th 2009, 06:08 PM
collegestudent321
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!
• Nov 1st 2009, 06:46 AM
Media_Man
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.

$x_1=y^2, x_2=y+2$ has intersection points $(1,-1),(2,4)$. So the integral is $A=\int_{-1}^2 y+2-y^2 dy$. Multiplying this result by the constant density $\rho=3$ does indeed get you a correct answer.