1.

Find \(\int \frac{dx}{\sqrt{5-x^2}}\).(a) \(sin^{-1}⁡\frac{x}{\sqrt{5}}+C\)(b) \(2 sin^{-1}⁡\frac{x}{\sqrt{5}}+C\)(c) –\(sin^{-1}⁡\frac{x}{\sqrt{5}}+C\)(d) \(sin^{-1}⁡\frac{x}{5}+C\)This question was addressed to me during a job interview.Asked question is from Integrals of Some Particular Functions in portion Integrals of Mathematics – Class 12

Answer»

Right option is (a) \(SIN^{-1}⁡\FRAC{x}{\SQRT{5}}+C\)

Easy explanation: \(\int \frac{dx}{\sqrt{5-x^2}}=\int \frac{dx}{\sqrt{(√5)^2-x^2}}\)

By USING the formula \(\int \frac{dx}{\sqrt{a^2-x^2}}=sin^{-1}⁡\frac{x}{a}+C\)

∴\(\int \frac{dx}{\sqrt{x^2-5}}=sin^{-1}⁡\frac{x}{\sqrt{5}}+C\)


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