5.4 Indefinite Integrals and the Net Change Theorem/43

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int\limits_{-1}^{2}(x-2|x|)dx = \int\limits_{-1}^{0}(x-2(-x))dx + \int\limits_{0}^{2}(x-2(x))dx \\[2ex] &= \left(\frac{1}{2} {x^2} + x^2 \right)\bigg|_{-1}^{0} + \left(\frac{1}{2} {x^2} - x^2 \right)\bigg|_{0}^{2} \\[2ex] &= 0- \left(\frac{1}{2} (-1)^2 + (-1)^2 \right) + \left(\frac{1}{2} (2)^2 - (2)^2 \right) - 0 \\[2ex] &= \left(-\frac{1}{2} - 1\right) + \left(2 - 4\right) \\[2ex] &=-\frac{1}{2}-1-2 = -\frac{1}{2}-3 &= -3.5 \end{align} }