## anonymous 5 years ago find integral of Fdr where f(x,y)=(2xy)i+(x^2)j and C is the curve y=sqrt(x) between point (0,0) and (4,2)

1. anonymous

Parameterize with respect to a single variable. Try x. Then set up the integral from there.

2. anonymous

Dump in the parameterization

3. anonymous

APPLY GREENS THEOREM $\int\limits_{}^{}_cFdr=\int\limits_{0}^{2}\int\limits_{0}^{\sqrt{x}}(2x+2y)dydx$ $\int\limits_{0}^{2}(2x ^{3/2}+x)dx=4/5x ^{5/2}+1/2x^2|[0,2]=2+16/5\sqrt{2}$

4. anonymous

$16/5\sqrt{2}-2$ that should be the answer i forgot the 2x-2y, 2x^3/2-x