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NDA 2018 Maths · Mathematics · Integrals · easy

∫0^3(dx)/(√(9-x^2) equals

Single correct option

∫03dx9−x2\int_0^3\frac{dx}{\sqrt{9-x^2}} equals
  1. A. π6\frac\pi6
  2. B. π2\frac\pi2
  3. C. π\pi
  4. D. 13\frac13
Show answer and solution

Answer: (B) π2\frac\pi2

∫dxa2−x2=sin⁡−1xa\int\frac{dx}{\sqrt{a^2-x^2}}=\sin^{-1}\frac xa, so the value is sin⁡−11−sin⁡−10=π2\sin^{-1}1-\sin^{-1}0=\frac\pi2. The trap is to divide by aa as in ∫dxa2+x2\int\frac{dx}{a^2+x^2}; here no factor 1a\frac1a appears.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake