The graph of f is shown. Evaluate each integral by interpreting it in terms of areas.

Question

(a)

45

f(x)dx

0

Answer 1

From zero to 10 we have a trapezoid, from 10 to 15 is a rectangle, from 15 to 25 is a triangle, then, below the x-axis, from 25 to 35 is a triangle, and finally from 35 to 45 is a trapezoid, like this:

Area of A = 1/2(5 + 15)(10) = 100

Area of B = (5)(15) = 75

Area of C = 1/2(10)(15) = 75

Area of D = -1/2(10)(15) = -75

Area of E = -1/2(15 + 10)(10) = -125

Area Total = 100 + 75 + 75 - 75 - 125 = 50 so the integral = 50