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NDA 1 2024 Maths, question 74

Topic: Integral calculus

Q74

What is ∫−11(3sin⁡x−sin⁡3x)cos⁡2xdx\int _{-1}^{1}(3\sin x-\sin 3x)\cos ^{2}x dx equal to ?

  1. (a) −14-\frac{1}{4}
  2. (b) 00Correct answer
  3. (c) 12\frac{1}{2}
  4. (d) 14\frac{1}{4}

Solution.

Answer: (b) 00

  1. The integrand is odd on the symmetric interval and has no singularity there.
  2. Values at x and −x cancel, so the definite integral is zero.