Q. 14 - Calculus

Question

Repeat Exercise 13 for the function $f$ shown above at the right, on the interval $[-2,2].$

Step-by-Step Solution

Answer

Part (a) 

Part (b) ${\int }_{-2}^{-1.5}\left(f\right(x)-g(x\left)\right)dx+{\int }_{-1.5}^{0.5}\left(g\right(x)-f(x\left)\right)dx+{\int }_{0.5}^2\left(f\right(x)-g(x\left)\right)dx$

Part (a) Step 1. Calculation

The rectangles can be drawn as

Part (b) Step 1. Calculation

The given graph is 

The area can be calculated as:

${\int }_{-2}^{-1.5}\left(f\right(x)-g(x\left)\right)dx+{\int }_{-1.5}^{0.5}\left(g\right(x)-f(x\left)\right)dx+{\int }_{0.5}^2\left(f\right(x)-g(x\left)\right)dx$