Hey everyone,

I have to evaluate F=<2+x^{2},3xy> where a curve is formed by moving along x^{2}+ y^{2}= 4 from (2,0) to (0,2)

then along the line segment from (0,2) to (-1,0)

So far I've parameterized the first curve as r(t)=<2cost(t), 2sin(t)>, taking the derivative of that to get my tangent vector.

Then I parameterized F(r(t)) to get F(r(t))=<2+ 4cos(t)^2, 12cos(t)sin(t)>

Dotted my new F and tangent vector to get 16cos(t)^{2}sin(t) - 4sin(t) and took the integral from 0 to pi/2

For this I got: -28/3, wolfram got 4/3

For the second curve I set r(t) = < -t, 2-2t> from 0 to 1 and got the tangent vector as <-1,-2>

My new F is F(r(t))=<2+t^2, 6t^{2}-6t>

I dotted those to get 12t - 13t^2 - 2 and took the integral from 0 to 1

For this I got -1/3 and wolfram got -1/3

Adding these I got -29/3 and wolfram got 1, neither of these is what it's supposed to be, I guess the answer is -17/3 but I can't find how to get that anyway!

All help is greatly appreciated! Really really confused...