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Find the value of b if \(\rm \int \frac{dx}{\sqrt {9-x^{2}}}=sin^{-1}\frac{x}{b}+C\)
1. 2
2. 3
3. 4
4. 5
5. None of these

1 Answer

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Best answer
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.

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