Using Green's Theorem to evaluate the line integral below....?

Question

Use Green's Theorem to evaluate the line integral

ò P(x, y) dx+ Q(x, y) dy
C

ò = integral

where C is the path from (0, 0) to (1, 0) along y= 0; then from (1, 0) to (1, 1) along x = 1; then from (1, 1) to (0, 0) along y= x^1/2, given that P(x, y) = y^5, and
Q(x, y) = 6xy.

a. 1
b. 11/10
c. 7/6
d. 17/14
e. 5/4
f. 23/18
g. 13/10
h. 29/22
i. 4/3

or is it none of these?

Answer 1

Hi Amber,

Again using repeated line integrals rather than Green's Thm (which I'm not remembering) I have arrived at an answer to your problem. I came up with answer d, or 17/14. However, I don't guarantee that it's correct. My Calc III is unfortunately a little rusty these days!

Hope that helps.

Answer 2

I get d. See http://img474.imageshack.us/img474/1816/lineintegralpm4.png