Question

Let F= 6(x+y)i + 8 sin(y)j,. Find the line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order.

line integral =

Answer 1

The line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order is -333.06456

How to determine the line integral of F around the perimeter?

The F can be rewritten as

F(x,y) = [6(x+y) , 6sin(y)

The path C on which we are going to evaluate the integral is