Chapter 14, Problem 40RE

(a)

To determine

To graph: The graph of function $f\left(x\right)=2x+3$ at the interval $\left[0,4\right]$.

(b)

To determine

To calculate: The approximate area under the function $f\left(x\right)=2x+3$ on the interval $\left[0,4\right]$ by partitioning the interval $\left[0,4\right]$ into four subintervals of equal length and choosing the left end point of each subinterval.

(c)

To determine

To calculate: The approximate area under the function $f\left(x\right)=2x+3$ on the interval $\left[0,4\right]$ by partitioning the interval $\left[0,4\right]$ into four subintervals of equal length and choosing the right end point of each subinterval.

(d)

To determine

To calculate: The approximate area under the function $f\left(x\right)=2x+3$ on the interval $\left[0,4\right]$ by partitioning the interval $\left[0,4\right]$ into eight subintervals of equal length and choosing the left end point of each subinterval.

(e)

To determine

To calculate: The approximate area under the function $f\left(x\right)=2x+3$ on the interval $\left[0,4\right]$ by partitioning the interval $\left[0,4\right]$ into eight subintervals of equal length and choosing the right end point of each subinterval.

(f)

To determine

To calculate: The actual area under the function $f\left(x\right)=2x+3$.