
line integrals
ok...Compute the line integral bounded by C of ydx  xdy (i dont know if that was a typo if thats normal, ive never seen an integral like that)
where C is the upper semicircle of radius 1 oriented from (1; 0) to (1; 0) (i.e. counterclockwise).
$\displaystyle \int xdy  ydx$
when i did the problem i got 0 as the answer, but my teachers answer page says Pi. any ideas?
also i used C = <cos t, sin t> from 0 to Pi.

Is the problem the integral of $\displaystyle y\,dxx\,dy$ or $\displaystyle x\,dyy\,dx$? In your stating words, you have the first, but for your formula you wrote the second. These two have opposite signs, and will give opposite answers. I think you mean the first, as that gives the answer you gave:
Your parametrization gives $\displaystyle x(t)=\cos{t}$, $\displaystyle y(t)=\sin{t}$, and thus $\displaystyle \frac{dx}{dt}=\sin{t}$ and $\displaystyle \frac{dy}{dt}=\cos{t}$. Thus we have:
$\displaystyle \int_{C}y\,dxx\,dy=\int_0^{\pi}\left(y\frac{dx}{dt}x\frac{dy}{dt}\right)\,dt$
$\displaystyle =\int_0^{\pi}\sin{t}\cdot(\sin{t})\cos{t}\cdot\cos{t}\,dt$
$\displaystyle =\int_0^{\pi}\sin^2{t}\cos^2{t}\,dt$
$\displaystyle =\int_0^{\pi}(1)\,dt$
$\displaystyle =\int_0^{\pi}\,dt$
$\displaystyle =\pi$
Kevin C.