6.1 Areas Between Curves/21: Difference between revisions
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File:6.1number21.png | [[File:6.1number21.png|right|600px|]] | ||
<math> | |||
\begin{align} | |||
x&=1-y^2, x=y^2-1 \\[1ex] | |||
A &= \int_{a}^{b}[x_R-x_L]dy=\int_{1}^{-1}[(1-y^2)-(y^2-1)]dy\\[2ex] | |||
&=\int_{1}^{-1}[2-2y^2]dy=[2y-2(\frac{y^3}{3})|_{-1}^{0}\\[2ex] | |||
&=2(1)-2(\frac{(1)^3}{3})-[2(-1)-2(\frac{(-1)^3}{3})]\\[2ex] | |||
&=2-\frac{2}{3}+2-\frac{2}{3}\\[2ex] | |||
&=\frac{8}{3} | |||
\end{align} | |||
</math> | |||
Latest revision as of 19:51, 22 September 2022
![{\displaystyle {\begin{aligned}x&=1-y^{2},x=y^{2}-1\\[1ex]A&=\int _{a}^{b}[x_{R}-x_{L}]dy=\int _{1}^{-1}[(1-y^{2})-(y^{2}-1)]dy\\[2ex]&=\int _{1}^{-1}[2-2y^{2}]dy=[2y-2({\frac {y^{3}}{3}})|_{-1}^{0}\\[2ex]&=2(1)-2({\frac {(1)^{3}}{3}})-[2(-1)-2({\frac {(-1)^{3}}{3}})]\\[2ex]&=2-{\frac {2}{3}}+2-{\frac {2}{3}}\\[2ex]&={\frac {8}{3}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/935c1ac592577507854d86113c846145dc1b477c)