Consider the function f(x)= cases x^ 2 -1, & 0 x 1, 2-x, & 1< x 3

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the function

f(x)=\begin{cases} x^{2}-1, & 0\le x\le 1,\\ 2-x, & 1< x\le 3. \end{cases}

Which of the following integral expressions equals the area of the region bounded by the graph of

f

and the

x

–axis on

0\le x\le 3

? (a)

\displaystyle\int_{0}^{1}(1-x^{2})\,dx+\int_{1}^{3}(2-x)\,dx

(b)

\displaystyle\int_{0}^{1}|x^{2}-1|\,dx+\int_{1}^{3}|2-x|\,dx

(c)

\displaystyle\int_{0}^{1}|x^{2}-1|\,dx+\int_{1}^{2}(2-x)\,dx

(d)

\displaystyle\int_{0}^{1}(x^{2}-1)\,dx+\int_{1}^{3}(2-x)\,dx