Answer
(b) 0.46
(a) 0.45
Work Step by Step
(a)
$0.4514=\frac{0.56+0.45+0.35+0.25+0.16+0.74+0.65}{7}$
(b)
Using the definition of $f_{\text {ave}}$:
$f_{a v e}=\frac{1}{-a+b} \int_{a}^{b} f(x) d x$
Thus:
$\frac{1}{7} \int_{0}^{7}(0.5 \sin (2.481+0.213 x)+0.5) d x=\frac{1}{7} \int_{2.481}^{3.972} \frac{(0.5 \sin u+0.5)}{0.213} d u \approx$
$\frac{3.23}{7} \approx 0.46$
