Skip to main contentSkip to solution

Area bounded by the curves

y={x+2,x≥−1−x,x<−1y=\begin{cases}x+2, & x\ge-1\\-x, & x<-1\end{cases}, x=−2,x=3x=-2, x=3 and y=0y=0 is:

Solution

✅ Correct Option: 2

On [−2,−1)[-2,-1) the curve is y=−xy=-x, giving area ∫−2−1(−x)dx=32\int_{-2}^{-1}(-x)dx=\frac{3}{2}.

On [−1,3][-1,3] the curve is y=x+2y=x+2, giving area ∫−13(x+2)dx=12\int_{-1}^{3}(x+2)dx=12.

The total area is 32+12=272\frac{3}{2}+12=\frac{27}{2} square units.

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question