Chapter 5, Problem 6E

a.

To determine

To write: The integral ${\displaystyle {\int }_0^3{e}^{-\frac{x}{2}}dx}$ as a limit of Reimann sums, taking the sample points to be right endpoints.

b.

To determine

To calculate: The integral ${\displaystyle {\int }_0^3{e}^{-\frac{x}{2}}dx}$ using midpoint rule with six subintervals.

c.

To determine

To calculate: The integral ${\displaystyle {\int }_0^3{e}^{-\frac{x}{2}}dx}$ using Fundamental theorem. Also compare with ${\displaystyle {\int }_0^{3}f\left(x\right)dx}\approx 1.550$