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NDA 1 2024 Maths, question 90

Topic: Integral calculus

Passage · Q89 to Q90

Let φ(a)=∫aa+100π∣sin⁡x∣dx\varphi(a)=\int _{a}^{a+100\pi}|\sin x| dx

Q90

What is φ′(a)\varphi'(a) equal to ?

  1. (a) 00Correct answer
  2. (b) π\pi
  3. (c) 100100
  4. (d) 200200

Solution.

Answer: (a) 00

  1. By differentiation of an integral with moving endpoints, φ′(a) = |sin(a + 100π)| − |sin a| = 0.
  2. This also follows because φ(a) is the constant 200.