Chapter 14, Problem 42RE

(a)

To determine

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

(b)

To determine

Approximate area $A$ by partitioning $\left[1,4\right]$ into three subintervals of equal width and choosing $u$ as the left endpoint of each subinterval.

(c)

To determine

Approximate area $A$ by partitioning $\left[1,4\right]$ 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 ${\displaystyle \underset{1}{\overset{4}{\int }}\left(\frac{1}{x^2}\right)}dx$ using graphing utility.