Question

Consider the following line integral along the given positively oriented curve. ∫Cyexdx+2exdy, C is the rectangle with vertices (0,0),(6,0),(6,5), and (0,5) Use Green's theorem to write an equivalent iterated integral. ∫Cyexdx+2e2dy=∫0___(∫0)___ (____)dy dx Use Green's theorem to evaluate the line integral.

______

Answer 1

To use Green's theorem to evaluate the line integral ∫C (yex dx + 2e^x dy), you first need to find the equivalent double integral over the region bounded by the curve C. Green's theorem relates a line integral over a closed curve to a double integral over the region enclosed by that curve. The formula for Green's theorem is as follows:

∫C (P dx + Q dy) =

Explanation: