1.

Find \(\int \frac{cos^{-1}x}{\sqrt{1-x^2}} dx\).(a) \(\frac{(sin^{-1}⁡x)^2}{2}+C\)(b) \(\frac{(cos^{-1}⁡x)^2}{7}+C\)(c) \(\frac{(cos^{-1}⁡x)^2}{2}+C\)(d) –\(\frac{(cos^{-1}⁡x)^2}{2}+C\)I had been asked this question at a job interview.This interesting question is from Methods of Integration-1 in division Integrals of Mathematics – Class 12

Answer» CORRECT CHOICE is (c) \(\frac{(cos^{-1}⁡X)^2}{2}+C\)

For explanation I would say: Let cos^-1⁡x=t

Differentiating w.r.t x, we GET

\(\frac{1}{\sqrt{1-x^2}} dx=dt\)

∴\(\int \frac{cos^{-1}⁡x}{\sqrt{1-x^2}} dx=\int t dt\)

=\(\frac{t^2}{2}\)

Replacing t with cos^-1x,we get

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


Discussion

No Comment Found

Related InterviewSolutions