- #1
jonroberts74
- 189
- 0
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