Chapter 4.3, Problem 62P

(a)

To determine

To algebraically prove ${\displaystyle \underset{1}{\overset{3}{\int }}(\text{3x + 4})\text{dx = 20}}$ by calculating a limit of Riemann sums.

(b)

To determine

To geometrically prove ${\displaystyle \underset{1}{\overset{3}{\int }}(\text{3x + 4})\text{dx = 20}}$ by recognizing the region as a trapezoid and calculating its area

(c)

To determine

To prove that ${\displaystyle \underset{1}{\overset{3}{\int }}(\text{3x + 4})\text{dx = 20}}$ with the formulas, by using the properties and formulas of definite integrals.