Find the value of b if \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\)

Question

Question

Answer 1

Concept:

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

Calculation:

Given: \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\)

Using the formula,

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

\(\rm \Rightarrow \int \frac{dx}{\sqrt {9-x^{2}}}=\int \frac{dx}{\sqrt {3^{2}-x^{2}}}=sin^{-1}\frac{x}{3}+C\) -----(1)

∵ It is given that, \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\)- ----(2)

On comparing (1) and (2) we get b = 3.

Hence, the correct answer is option 2.