Answer
$\frac{1}{2}$
Work Step by Step
Step 1. The limit of the Riemann sum leads to a definite integral, and from the expression given in the exercise, we can identify that $f(x)=sin(x)cos(x)$ and the interval is $[0,\pi/2]$.
Step 2. We can write the integral as
$\int_0^{\pi/2}f(x)dx=\int_0^{\pi/2}sin(x)cos(x)dx$
Step 3. Using substitution, let $u=sin(x)$, and we have $du=cos(x)dx$ with $x\to0, u\to0$ and $x\to \pi/2, u\to1$
Step 4. We have
$\int_0^{\pi/2}f(x)dx=\int_0^1(u)du=\frac{1}{2}u^2|_0^1=\frac{1}{2}$
