Chapter 5.2, Problem 24E

(a)

To determine

An approximation to the integral, ${\displaystyle \underset{0}{\overset{4}{\int }}\left(x^2-3x\right)dx}$ using a Riemann sum with 8 subintervals and sample points as right endpoints.

(b)

To determine

To sketch: The diagram of the approximation of the integral, ${\displaystyle \underset{0}{\overset{4}{\int }}\left(x^2-3x\right)dx}$.

(c)

To determine

The value of the integral, ${\displaystyle \underset{0}{\overset{4}{\int }}\left(x^2-3x\right)dx}$ using the Theorem.

(d)

To determine

To interpret: The integral, ${\displaystyle \underset{0}{\overset{4}{\int }}\left(x^2-3x\right)dx}$ in terms of it’s area with the help of a diagram.