[Math] Write an integral to represent the area of the shaded portion of the rectangle shown in Figure 1.

Question

Can someone please help me with this question? I've no idea how I'm supposed to do that with an integral:

Write an integral to represent the area of the shaded portion of the rectangle shown in Figure 1. Check your answer.

Thank you!

Answer 1

The shaded area would be equal to the integral for the area under the upper "curve" ([-1,1] to [1,3]) less the integral for the area for the lower "curves" ([-1,1] to [0,0] and [0,0] to [1,1] also known as f(x)=|x|).