Let A 7 5 B 5 8 C 3 1 and D 0 1 Let fx be the function w

Let A = (-7, 5), B = (-5, -8), C = (-3, 1), and D = (0, -1). Let f(x) be the function whose graph consists of the three line segments , and Evaluate the definite integral by interpreting it in terms of signed area. Suggestion: Draw a picture of the region whose signed area is represented by the integral. Then find the signed area using formulas from high school geometry.

Solution

int(-7,0) = int(-7,-5) + int(-5,-3)+int(-3,0) = 1/2*13*2 - 1/2*2*9 +1/2*3*2 = 7