Chapter 7 - Applications of Integration - 7.1 Exercises - Page 442: 13

Matches $(d)$

Given $$f(x)= x+1, \ g(x)=(x-1)^2$$ To determine the area between the curves $f(x)= x+1, \ g(x)=(x-1)^2$ first we get the intersection points, by solving the following equations $y= x+1, \ y=(x-1)^2$ we get $(0,1),(3,4)$ So, \begin{align} A&=\int_ 0^3 (x+1-(x-1)^2) \ dx \\ &=\left[\frac{x^2}{2}+x-\frac{(x-1)^3}{3}\right]_0^3\\ &=4.5\approx 4 \end{align}