Question

Verify Green's Therom by evaluating both integrals:
y^2dx+x^2dy for the given path.

C:boundary of the region lying between the graphs of y=c and y=square root of x

Answer 1

Verify Green's Therom by evaluating both integrals:
\[\int\limits_{C}^{}y^2dx+x^2dy=\int\limits_{R}^{}\int\limits_{}^{}(\frac{DN}{Dx}-\frac{DM}{Dy}) dA\] for the given path.

C:boundary of the region lying between the graphs of \[y=x\] and \[y=\sqrt{x}\]

Answer 2

Thats the rewrite of the problem. I've set up the integrals and want to see if I've done it correct. First I'll draw my images of the functions.

Answer 3

The arrows are the orientation of both functions.