6.1 Areas Between Curves/14: Difference between revisions
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\begin{align} | \begin{align} | ||
& y=\cos(x), y=2-\cos(x)\\ | & \color{purple}\mathbf{y=\cos(x)}, y=2-\cos(x)\\ | ||
& \int_{0}^{2\pi} \left[2 - \cos(x) - \cos(x) \right]\mathrm{d}x = \int_{0}^{2\pi} \left[2 - 2\cos(x)\right]\mathrm{d}x\\ | & \int_{0}^{2\pi} \left[2 - \cos(x) - \cos(x) \right]\mathrm{d}x = \int_{0}^{2\pi} \left[2 - 2\cos(x)\right]\mathrm{d}x\\ | ||
&= \left[ 2x-2\sin(x) \right]\bigg|_{0}^{2\pi}\\ | &= \left[ 2x-2\sin(x) \right]\bigg|_{0}^{2\pi}\\ | ||
Revision as of 19:37, 20 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\color {purple}\mathbf {y=\cos(x)} ,y=2-\cos(x)\\&\int _{0}^{2\pi }\left[2-\cos(x)-\cos(x)\right]\mathrm {d} x=\int _{0}^{2\pi }\left[2-2\cos(x)\right]\mathrm {d} x\\&=\left[2x-2\sin(x)\right]{\bigg |}_{0}^{2\pi }\\&=\left(4\pi -0\right)-\left(0\right)\\&=4\pi \end{aligned}}}