Let . Which of the following rewrites without the absolute value sign so that the…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

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

Related theory

Browse the problem library