Let p (x, y) = e x * siny+3 y, q (x, y) = e x * cosy-2x. Using Green's formula,
The integral of the original integral expression on the closed curve l' is equal to
{the partial derivative of q (x, y) about x minus the partial derivative of P(x, y) about y} = (e x * cosy-2)-(e x * cosy+3) =-5.
The double integral on the semicircle surrounded by l' is equal to 5 * pai (3/2) 2/2 = (45/8) pai.
The original integral is equal to the integral on L' minus the integral on a segment of T on the X axis with abscissa of 1 to 7. Note that if y=0 and dy=0 on t are substituted into the integrand expression, the integral on t section is 0, so the obtained integral value is (45/8)pai.