6.1 Areas Between Curves/25

${\begin{aligned}&\color {red}\mathbf {y=x^{2}} &\color {royalblue}\mathbf {y={\frac {2}{({x^{2}}+1)}}} \\\end{aligned}}$

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] &= \left[\frac{2\pi}{4}-\frac{1}{3}\right] - \left[-\frac{2\pi}{4} \\[2ex] \end{align} }