Question

Find the Riemann sum of f(x) = sinx on [-p,p]by using four subintervals of equal length and midpoint rule?

Answer 1

`0`

Explanation:

We have `f(x)=sinx` and so:

`f(-x)=sin(-x) = -sinx`

Hence, `f(x)` is an odd function and has rotational symmetry about the origin, thus we do not need to perform any calculation, and we immediately deduce that

`int_-p^p f(x) = 0`