6.1 Areas Between Curves/16
16)
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} & \color{red} \mathbf{y=x^3-x} & \color{royalblue}\mathbf{y=3x} \\ \end{align} }
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} x^3-x &= 3x \\ x^3 &=4x \\ x^2(x) &=4(x) \\ x^2 &=4 \\ x &=\sqrt{4}\\ x &= \pm2 \\[2ex] \int_{-2}^{2} [(x^3-x)-(3x)]dx=\int_{-2}^{2} [x^3-4x]dx \\[2ex] =\left[\frac{x^4}{4}-2x^2\right]\Bigg|_{-2}^{2}\\[2ex] =\frac{(2)^4}{4}-2(2)^2-\left(\frac{(-2)^4}{4}-2(-2)^2\right)\\[2ex] =\frac{16}{4}-2(4)-(\frac{16}{4}-2(4))\\[2ex] =4-8-(4-8)\\[2ex] =-4-(-4)\\[2ex] =-4+4\\[2ex] =0 \end{align} }