6.1 Areas Between Curves/16: Difference between revisions
(Created page with "right|350px| 16) <math> \begin{align} & \color{red} \mathbf{y=x^3-x} & \color{royalblue}\mathbf{y=3x} \\ \end{align} </math> <math> \begin{align} x^3-x &= 3x \\ x^3 &=4x \\ x^2(x) &=4(x) \\ x^2 &=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...") |
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x^2 &=4 \\ | x^2 &=4 \\ | ||
x &=\sqrt{4}\\ | |||
x &= \pm2 \\[2ex] | x &= \pm2 \\[2ex] | ||
Revision as of 20:35, 18 September 2022
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 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}x^{3}-x&=3x\\x^{3}&=4x\\x^{2}(x)&=4(x)\\x^{2}&=4\\x&={\sqrt {4}}\\x&=\pm 2\\[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{aligned}}}