If $\int \frac{1}{\sqrt{2 a x-x^2}} d x=fog(x)+C$, then

$f(x)=\cos ^{-1} x$, and $g(x)=\frac{x-a}{a}$

$f(x)=\tan ^{-1} x$ and $g(x)=\frac{x-a}{a}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \frac{1}{\sqrt{2 a x-x^2}} d x=fog(x)+C

, then

View answer and explanation

Correct option: B

f(x)=\sin ^{-1} x

, and

g(x)=\frac{x-a}{a}

Option B,

f(x)=\sin ^{-1} x

, and

g(x)=\frac{x-a}{a}

, is correct because completing the square and using a trigonometric substitution leads to this result.

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