Verify that the area function in Example 2c gives the correct area when x = 6 and x = 10.

Example 2 Area of a Trapezoid

Consider the trapezoid bounded by the line f ( t ) = 2 t + 3 and the t-axis from t = 2 to t = x (Figure 5.38). The area function A ( x ) = ∫ 2 x f ( t ) d t gives the area of the trapezoid, for x ≥ 2.

a.    Evaluate A(2).

b.    Evaluate A(5).

c.    Find and graph the area function y = A(x), for x ≥ 2.

d.    Compare the derivative of A to f.