(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int_C \mathbf F\cdot d \mathbf r[/tex] where [tex]\mathbf F = x^2\vec{i}+e^{\sin^4{y}}\vec{j}[/tex]

and C is the segment of y=x^2 from (-1,1) to (1,1).

2. Relevant equations

[tex]\int_C \mathbf F\cdot d \mathbf r=\int_a^b \mathbf F( \mathbf r(t))\cdot r'(t) dt=\int_C Pdx+Qdy[/tex] where [tex]\mathbf F = P\vec{i}+Q\vec{j}[/tex]

3. The attempt at a solution

I parametrize C:

[tex]\mathbf r(t)=<t,t^2>|-1\leq t \leq 1[/tex]

Well, I know how to apply the equations above as well as Green's theorem (I use this by letting C2 be a line from (1,1) to (-1,1) and integrating across the enclosed disk D), but no matter what I do, I find myself having to integrate some version of [tex]e^{\sin^4{y}}[/tex]

There has to be some trick I'm missing. Could someone point me in the right direction?

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# Homework Help: Line integral across a vector field

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