Posted by **Josh** on Tuesday, November 8, 2011 at 11:55pm.

Find the double integral of f (x, y) = (x^7)y over the region between the curves y = x^2 and y = x(3 - x).

- Math - Calculus III -
**Steve**, Wednesday, November 9, 2011 at 5:38am
The curves intersect at (0,0) and (3/2,9/4)

So, we want

Int[0,3/2] Int[x^2,3x-x^2] (x^7 y) dy dx

= Int[0,3/2] (x^7 y^2)/2 [x^2,3x-x^2] dx

= Int[0,3/2] (1/2)(9x^9 - 6x^10) dx

= 1/2(9/10 x^10 - 6/11 x^11)[0,3/2]

= 1/2 (3/2)^10 (9/10 - 6/11 * 3/2)

= 1/2 (3/2)^10 (9/110)

= 531441/225280 = 2.359

## Answer This Question

## Related Questions

- Math - Find the double integral of f (x, y) = (x^7)y over the region between the...
- Calculus - Evaluate the surface integral. the double integral of (x^2 + y^2 + z^...
- Calculus (double integral) PLEASE HELP! - Evaluate double integral ln((x-y)/(x+y...
- double integral - 1. Sketch the region of integration & reverse the order of ...
- Calculus - 1. Find the are between the curves y=e^x and y=4-x^2 graphically. a...
- Calculus-Area between curves - Sketch the region enclosed by the given curves. ...
- Calculus - Find the volume of the solid whose base is the region in the xy-plane...
- calculus - Find the area of the region using the method that requires you to ...
- Calculus - Can someone look over my work and tell me if my steps look correct? I...
- calculus - LEt f and g be continous functions with the following properties i. ...

More Related Questions