Question

Use Green's Theorem to evaluate the line integral along the given positively oriented curve. C yex dx 2ex dy, C is the rectangle with vertices (0, 0), (3, 0), (3, 2), and (0, 2)

Answer 1

Answer:

2 ( e^3 + 1 )

Step-by-step explanation:

The path of the attached Rectangle is anti-clockwise

and the Integrand:  P( x, y ) dx +  q ( x , y ) dy

 P( x, y )  = ye^x

 q ( x , y ) = 2ex

hence :  dq/dx - dp/dy = 2e^x - e^x = e^x

attached below is the remaining  solution

using Green's theorem