Hi everyone.

I am going through examples for maths exams and am unsure on the final part of a question I am attempting so hoping you may help me?

What I have so far:


\theta (x,y,z) = x^2z^2+3yz+2x

hence

\nabla \theta (x,y,z) = (2xz^2+2, 3z, 2zx^2+3y)


The question:


Compute the closed line integral anticlockwise around the curves C1: y= \sqrt{x} and C2: y = x^2

How far Ive got:


So, using green's theorem

\oint \nabla \theta (x,y,z) dr

is the same as

\int_{y=x^2}^{y=\sqrt{x}}\int_0^1 \nabla \theta (x,y,z) dxdy

I think this is correct, but cant seem to find the next "step". Id be grateful if anyone could tell me if Im on the right track, and maybe show me where to go on the next step?

Thanks