Answer
a) 1.18347
b) 0.790766
Work Step by Step
a) $\Delta x=\frac{\frac{\pi}{2}-0}{4}=\frac{\pi}{8}$
$\sum_{i=0}^{3}\sin(\frac{\pi}{8}+\frac{\pi}{8}i)\frac{\pi}{8}=1.18347$
Because the function is concave down and right endpoints are used, the Riemann sum is an overestimate
b) $\Delta x=\frac{\frac{\pi}{2}-0}{4}=\frac{\pi}{8}$
$\sum_{i=0}^{3}\sin(\frac{\pi}{8}i)\frac{\pi}{8}=0.790766$
Because the function is concave down and left endpoints are used, the Riemann sum is an underestimate
