Evaluate the integral below by interpreting it in terms of areas in the figure.

Question

The areas of the labeled regions are A1= 6, A2=3, A3=1 and A4=2 V =  ⁷₃

Answer 1

Remember that the integral of the function is the "area under the curve." Specifically, this is the area between the function and the x-axis. If the function is negative, then the area is considered negative.

The bounds of integration are 3 and 7. These bounds coincide with the A2 and A3 regions.

V= A3-A2 because A2 is considered negative area.

V=1-3=-2