Write an integral to represent the area of the shaded portion of the rectangle shown in Figure 1.
By John Peck •
$\begingroup$
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!
$\endgroup$2 Answers
$\begingroup$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|).
$\endgroup$ $\begingroup$Hint: It is the area between the function $x\mapsto 2+x$ and $x\mapsto |x|$.
$\endgroup$
