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NDA 2021 Maths · Mathematics · Definite Integrals · hard

∫-2^2(x^5+x^2 dx is equal to

Single correct option

∫−22(x5+x2) dx\displaystyle\int_{-2}^{2}(x^5+x^2)\,dx is equal to
  1. A. 00
  2. B. 163\dfrac{16}{3}
  3. C. 83\dfrac{8}{3}
  4. D. 323\dfrac{32}{3}
Show answer and solution

Answer: (B) 163\dfrac{16}{3}

The odd part x5x^5 integrates to 00 over a symmetric interval, so the integral is ∫−22x2dx=2⋅83=163\int_{-2}^2x^2dx=2\cdot\dfrac83=\dfrac{16}{3}. The value 0 would apply if the integrand were wholly odd.
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Original question written in the NDA 2021 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