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)

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)

ganeshie8 · Answer

Green's theorem :

$\large      \oint_C      Mdx + Ndy  =  \iint_R (N_x - M_y ) dA$

ganeshie8 · Answer

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

ganeshie8 · Answer

evaluate