Chapter 13, Problem 41RE

(a)

To determine

To graph: The function $f\left(x\right)=4-x^2$ on the interval $\left[-1,2\right]$, and indicate the area $A$ under $f$ from $-1$ to $2$.

(b)

To determine

Approximate area $A$ by partitioning $\left[-1,2\right]$ into three subintervals of equal width and choosing $u$ as the left endpoint of each subinterval.

(c)

To determine

Approximate area $A$ by partitioning $\left[-1,2\right]$ into six subintervals of equal width and choosing $u$ as the left endpoint of each subinterval.

(d)

To determine

The expression of the area as an integral.

(e)

To determine

The approximation of an integral ${\displaystyle \underset{-1}{\overset{2}{\int }}\left(4-x^2\right)}dx$ using graphing utility.