Question

Use Green's Theorem to evaluate the line integral along the given positively oriented curve.




integral C (cos y dx + x^2 sin y) dy

C is the rectangle with vertices (0, 0), (4, 0), (4, 3), (0, 3)

Answer 1

Green's theorem :

\(\large \oint_C Mdx + Ndy = \iint_R (N_x - M_y ) dA\)

Answer 2

\[ \oint_C \cos y~ dx + x^2 \sin y~ dy = \iint_R (2x\sin y + \sin y )dA = \int \limits_{0}^{4} \int \limits_{0}^{3} (2x\sin y + \sin y ) dy dx\]

Answer 3

evaluate