Calculating the Integral of $\vec{F}\cdot\vec{c}\,\,'$

[jonroberts74]

Homework Statement

$\vec{c} = <\cos t, \sin t, 0>; 0 \le t \le \frac{\pi}{2}$

$\vec{F} = x\hat{i}-y\hat{j}+z\hat{k}$

Homework Equations

The Attempt at a Solution

$\vec{F}(\vec{c}(t)) = <\cos t, - \sin t, 0>$

$\vec{c}\,\,'(t) = <-\sin t, - \cos t, 0>$

$\displaystyle \int_{0}^{\pi/2} \vec{F}\cdot\vec{c}\,\,'(t)dt$

$\displaystyle \int_{0}^{\pi/2} [-\sin t\cos t + \sin t \cos t]dt = 0$

the answer should be -1 not 0 according to the book

If $\displaystyle \int_{0}^{\pi/2} [-\sin t\cos t + \sin t \cos t]dt = 0$ was $\displaystyle \int_{0}^{\pi/2} [-\sin t\cos t - \sin t \cos t]dt = -1$ then it would be correct

 

[LCKurtz]

Check $c'(t)$.

 

[jonroberts74]

Check $c'(t)$.

ah, I know what I was doing, I was looking at $\vec{F}(\vec{c}(t)))$ when I was taking the derivative. silly