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_{-1}^{2}(x-2|x|)dx &= \int_{-1}^{0}(x-2(-x))dx + \int_{0}^{2}(x-2(x))dx = \int_{-1}^{0}3x\,dx - \int_{0}^{2}x\,dx \\[2ex] &= \left(\frac{3x^2}{2} \right)\bigg|_{-1}^{0} - \left(\frac{x^2}{2} \right)\bigg|_{0}^{2} \\[2ex] &= \left[\frac{3(0)^2}{2}-\frac{3(-1)^2}{2}\right]-\left[\frac{(2)^2}{2} - \frac{(0)^2}{2}\right] \\[2ex] &= \left[-\frac{3}{2}\right]-\left[\frac{4}{2}\right] \\[2ex] &= -\frac{7}{2} \\[2ex] \end{align} }