<p>Show that $\int_{1}^{2}{\sqrt{1-\frac{1}{{{x}^{2}}}}}\mathrm{d}x=\sqrt{3}-\frac{\pi }{3}$ by using the substitution $\frac{1}{x}=\cos \theta $.</p>

Show that $\displaystyle\displaystyle \int_{1}^{2}{\sqrt{1-\frac{1}{{{x}^{2}}}}}\mathrm{d}x=\sqrt{3}-\frac{\pi }{3}$ by using the substitution $\frac{1}{x}=\cos \theta $.

Techniques of  Integration - General

Techniques of  Integration

H2 Math

International Baccalaureate Higher Level Mathematics

Evaluation of a Definite Integral Using Trigonometric Substitution

Evaluation of a Definite Integral Using Trigonometric Substitution

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