6.1 Areas Between Curves/25: Difference between revisions
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\int_{1}^{-1}\left(\frac{2}{({x^2}+1)}\right) - \left(x^{2}\right) dx = \int_{1}^{-1}\left(2\cdot\frac{1}{(x^{2}+1)}\right)-\left(x^{2}\right) dx \\[2ex] | \int_{1}^{-1}\left(\frac{2}{({x^2}+1)}\right) - \left(x^{2}\right) dx = \int_{1}^{-1}\left(2\cdot\frac{1}{(x^{2}+1)}\right)-\left(x^{2}\right) dx \\[2ex] | ||
= \left[2\arctan(x)-\frac{x^{3}}{3}\right]\Bigg|_{-1}^{1} | = \left[2\arctan(x)-\frac{x^{3}}{3}\right]\Bigg|_{-1}^{1} \\[2ex] | ||
= \left[2\arctan(1)-\frac{(1)^{3}}{3}\right]-\left[(2\arctan(-1)-\frac{(-1)^{3}}{3}\right] \\[2ex] | = \left[2\arctan(1)-\frac{(1)^{3}}{3}\right]-\left[(2\arctan(-1)-\frac{(-1)^{3}}{3}\right] \\[2ex] | ||
Revision as of 20:51, 23 September 2022
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^{2}} & \color{royalblue}\mathbf{y=\frac{2}{({x^2}+1)}} \\ \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} \int_{1}^{-1}\left(\frac{2}{({x^2}+1)}\right) - \left(x^{2}\right) dx = \int_{1}^{-1}\left(2\cdot\frac{1}{(x^{2}+1)}\right)-\left(x^{2}\right) dx \\[2ex] = \left[2\arctan(x)-\frac{x^{3}}{3}\right]\Bigg|_{-1}^{1} \\[2ex] = \left[2\arctan(1)-\frac{(1)^{3}}{3}\right]-\left[(2\arctan(-1)-\frac{(-1)^{3}}{3}\right] \\[2ex] \end{align} }