5.4 Indefinite Integrals and the Net Change Theorem/43: Difference between revisions
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<math> | <math> | ||
\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] | \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] | ||
</math> | |||
<math> = \left(\frac{1}{2} {x^2} + x^2 \right)\bigg|_{-1}^{0} + \left(\frac{1}{2} {x^2} - x^2 \right)\bigg|_{0}^{2} | |||
&= 0- \left(\frac{1}{2} (-1)^2 + (-1)^2 \right) + \left(\frac{1}{2} (2)^2 - (2)^2 \right) - 0 | &= 0- \left(\frac{1}{2} (-1)^2 + (-1)^2 \right) + \left(\frac{1}{2} (2)^2 - (2)^2 \right) - 0 | ||
&= \left(\frac{1}{2} + 1\right) + \left(\frac{1}{2} (4) - 4\right) | &= \left(\frac{1}{2} + 1\right) + \left(\frac{1}{2} (4) - 4\right) | ||
Revision as of 18:53, 30 August 2022
Failed to parse (syntax error): {\displaystyle \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] }
Failed to parse (syntax error): {\displaystyle = \left(\frac{1}{2} {x^2} + x^2 \right)\bigg|_{-1}^{0} + \left(\frac{1}{2} {x^2} - x^2 \right)\bigg|_{0}^{2} &= 0- \left(\frac{1}{2} (-1)^2 + (-1)^2 \right) + \left(\frac{1}{2} (2)^2 - (2)^2 \right) - 0 &= \left(\frac{1}{2} + 1\right) + \left(\frac{1}{2} (4) - 4\right) \end{align} }