Home / NDA / Questions / Integrals / Question NDA 2017 Maths · Mathematics · Integrals · medium
∫(dx)/(√(9-4x^2) is equal to Single correct option
∫ d x 9 − 4 x 2 \displaystyle\int\frac{dx}{\sqrt{9-4x^2}} ∫ 9 − 4 x 2 d x is equal to
A. sin − 1 2 x 3 + C \sin^{-1}\frac{2x}{3}+C sin − 1 3 2 x + C B. 1 2 sin − 1 2 x 3 + C \frac12\sin^{-1}\frac{2x}{3}+C 2 1 sin − 1 3 2 x + C C. 1 3 sin − 1 2 x 3 + C \frac13\sin^{-1}\frac{2x}{3}+C 3 1 sin − 1 3 2 x + C D. 1 2 sin − 1 x 3 + C \frac12\sin^{-1}\frac{x}{3}+C 2 1 sin − 1 3 x + C Show answer and solution Answer: (B) 1 2 sin − 1 2 x 3 + C \frac12\sin^{-1}\frac{2x}{3}+C 2 1 sin − 1 3 2 x + C
Write
9 − 4 x 2 = 3 2 − ( 2 x ) 2 9-4x^2=3^2-(2x)^2 9 − 4 x 2 = 3 2 − ( 2 x ) 2 and put
u = 2 x u=2x u = 2 x , so
d x = d u 2 dx=\frac{du}{2} d x = 2 d u . Then the integral is
1 2 sin − 1 u 3 = 1 2 sin − 1 2 x 3 \frac12\sin^{-1}\frac u3=\frac12\sin^{-1}\frac{2x}{3} 2 1 sin − 1 3 u = 2 1 sin − 1 3 2 x . Omitting the factor
1 2 \frac12 2 1 (from
d u = 2 d x du=2\,dx d u = 2 d x ) or the
2 2 2 inside the inverse sine are the usual slips.
Original question written in the NDA 2017 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