Question

Use Greens Theorem to evaluate integral x^2ydx - xy^2dy, where C is 0 ≤ y ≤ √9-x^2 with counterclockwise orientation

Answer 1

Explanation:

a circle will satisfy the conditions of Green's Theorem since it is closed and simple.

Let's identify P and Q from the integral

`P=x^2 y`, and
`Q= xy^2`

Now, using Green's theorem on the line integral gives,

`\oint\limits_C {x^2ydx-xy^2dy } =\iint\limits_D {y^2-x^2} \, dA\\\\`