Evaluate the integral for .

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Evaluate the integral

\displaystyle \int \frac{dx}{\sqrt{a^{2}-x^{2}}}

for

|x|<|a|

and

a>0

. (a)

\cos^{-1}\!\left(\dfrac{x}{a}\right)+C

(b)

\ln\left|x+\sqrt{a^{2}-x^{2}}\right|+C

(c)

\sin^{-1}\!\left(\dfrac{x}{a}\right)+C

(d)

\dfrac{1}{a}\tan^{-1}\!\left(\dfrac{x}{a}\right)+C

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