Chapter 14, Problem 15CT

(a)

To determine

To graph: The function $f$, where $f\left(x\right)=\sqrt{16-x^2}$ is nonnegative and continuous on the interval $\left[0,4\right]$.

(b)

To determine

Partition of interval $\left[0,4\right]$ into eight subintervals of equal width and choose $u$ as the left endpoint of each subinterval and use the partition to approximate the area under the graph of $f$ from $x=0$ to $x=4$

(c)

To determine

Exact area of the region under the graph of $f\left(x\right)=\sqrt{16-x^2}$ on the interval $\left[0,4\right]$ and compare it with approximation in part (b).