Chapter 5.2, Problem 40P

To determine

(a)

Use a calculator or computer to find ${\displaystyle {\int }_0^6\left(x^2+1\right)}dx$. Represent this value as the area under a curve.

To determine

(b)

Estimate ${\displaystyle {\int }_0^6\left(x^2+1\right)}dx$ using a left-hand sum with n = 3. Represent this sum graphically on a sketch of $f\left(x\right)=x^2+1$. Is this sum an overestimate or underestimate of the true value found in part 40 (a)?

To determine

(c)

Estimate ${\displaystyle {\int }_0^6\left(x^2+1\right)}dx$ using a right-hand sum with n = 3. Represent this sum on your sketch. Is this sum an overestimate or underestimate?