Question

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)

Answer 1

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

Answer 2

Dump in the parameterization

Answer 3

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

Answer 4

\[16/5\sqrt{2}-2\] that should be the answer

i forgot the 2x-2y,
2x^3/2-x