5.4 Indefinite Integrals and the Net Change Theorem/3: Difference between revisions

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<math>
<math>
\begin{align}
\int\cos^{3}xdx = \sin{x}-\frac{1}{3}\sin^{3}x+C
</math>


& \int\cos^{3}xdx = \sin{x}-\frac{1}{3}\sin^{3}x+C \\[2ex]


& \frac{d}{dx} {[\sin{x} - \frac{1}{3} \sin^3{x} +C]} \\[2ex]
<math>
\begin{align}


& ={\cos{x} - \frac{1}{3}\cdot 3\sin^2{x} \cos{x} +0} \\[2ex]
\frac{d}{dx} {[\sin{x} - \frac{1}{3} \sin^3{x} +C]} &= {\cos{x} - \frac{1}{3}\cdot 3\sin^2{x} \cos{x} +0} \\[2ex]


& =\cos{x} - \sin^2{x}\cos{x} \\[2ex]
& =\cos{x} - \sin^2{x}\cos{x} \\[2ex]


& =\cos{x} - (1-cos^2(x))\cos{x} \\[2ex]
& =\cos{x} - (1-cos^2{x})\cos{x} \\[2ex]


& = \cos^3{x}


\end{align}
</math>


& = \cos^3{x}


 
Note: <math>
\end{align}
1-\cos^2(x) = \sin^2(x)
</math>
</math>

Latest revision as of 19:38, 21 September 2022



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