Mathematics

Mathematics

Problem

Let I=∫−23∣x−1∣ dxI=\displaystyle \int_{-2}^{3} |x-1|\,dx. Which of the following rewrites II without the absolute value sign so that the integrands are non-negative on each sub-interval? a) I=∫−21(x−1) dx+∫13−(x−1) dx\displaystyle I= \int_{-2}^{1} (x-1)\,dx + \int_{1}^{3} -(x-1)\,dx b) I=∫−21−(x−1) dx+∫13(x−1) dx\displaystyle I= \int_{-2}^{1} -(x-1)\,dx + \int_{1}^{3} (x-1)\,dx c) I=∫−21(x−1) dx+∫13(x−1) dx\displaystyle I= \int_{-2}^{1} (x-1)\,dx + \int_{1}^{3} (x-1)\,dx d) I=∫−20−(x−1) dx+∫03(x−1) dx\displaystyle I= \int_{-2}^{0} -(x-1)\,dx + \int_{0}^{3} (x-1)\,dx

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