Correct Answer - Option 2 : 3
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.
