Answer:
18
Step-by-step explanation:
The integral is the area between f(x) and the x-axis. Remember that area below the x-axis is negative.
The area between x=0 and x=6 is a trapezoid.
The area between x=6 and x=9 is a rectangle.
The area between x=9 and x=15 is a triangle.
The area between x=15 and x=21 is a triangle.
The area between x=21 and x=27 is a trapezoid.
A = ½ (3+9) (6) + (3)(9) + ½ (6)(9) + ½ (6)(-9) + ½ (-9+-6) (6)
A = 36 + 27 + 27 − 27 − 45
A = 18
