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NDA 2023 Maths · Mathematics · Definite Integrals · medium

The value of the definite integral of the function sin ^2xcos x over the symmetric interval from -(π)/(2) to (π)/(2) is

Single correct option

The value of the definite integral of the function sin⁡2xcos⁡x\sin^2x\cos x over the symmetric interval from −π2-\dfrac\pi2 to π2\dfrac\pi2 is
  1. A. 13\dfrac13
  2. B. 00
  3. C. 22
  4. D. 23\dfrac23
Show answer and solution

Answer: (D) 23\dfrac23

Put u=sin⁡xu=\sin x: the integral is ∫−11u2du=23\int_{-1}^{1}u^2du=\dfrac23. The integrand is even (since sin⁡2x\sin^2x and cos⁡x\cos x are both even), so it is not zero. The value 13\dfrac13 is half of the correct value.
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Original question written in the NDA 2023 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