Techniques of Integration - Integration by Substitution

Techniques of Integration - Integration by Substitution

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By considering \(x=4\cos \theta \) where \(0\le \theta \le \pi \), find \(\displaystyle\displaystyle \displaystyle\int{\sqrt{16-{{x}^{2}}}\,\mathrm{d}x}\).

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Answer:\(-8\cos^{-1}\left(\frac{x}{4}\right)+\frac12x\sqrt{16-x^2}+C\)

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