Mathematics

Mathematics

Problem

Consider the function f(x)={x2−1,0≤x≤1,2−x,1<x≤3.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 ff and the xx–axis on 0≤x≤30\le x\le 3? a) ∫01(1−x2) dx+∫13(2−x) dx\displaystyle\int_{0}^{1}(1-x^{2})\,dx+\int_{1}^{3}(2-x)\,dx b) ∫01∣x2−1∣ dx+∫13∣2−x∣ dx\displaystyle\int_{0}^{1}|x^{2}-1|\,dx+\int_{1}^{3}|2-x|\,dx c) ∫01∣x2−1∣ dx+∫12(2−x) dx\displaystyle\int_{0}^{1}|x^{2}-1|\,dx+\int_{1}^{2}(2-x)\,dx d) ∫01(x2−1) dx+∫13(2−x) dx\displaystyle\int_{0}^{1}(x^{2}-1)\,dx+\int_{1}^{3}(2-x)\,dx

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