Question

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 1

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

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