Evaluating the integral of $f(x, y)=yx$ Evaluate the integral $I = \int_C f(x,y) ds$ where $f(x,y)=yx$. and the curve $C$ is given by $x=\sin(t)$ and $y=\cos(t)$ for $0\leq t\leq \frac{pi}{2}$. I got the answer for this as $\frac{\sqrt{2}}{2}$ is that right?

Evaluate the parameterized integral
$$ \int_0^{\pi/2} \cos t \sin t \sqrt{\cos^2 t + \sin^2 t} \, dt = \int_0^{\pi/2} \cos t \sin t \, dt. $$
I don't see a square root of 2 appearing anywhere.
