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NDA 1 2024 Maths, question 89

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

Q89

What is φ(a)\varphi(a) equal to ?

  1. (a) 00
  2. (b) aa
  3. (c) 100a100a
  4. (d) 200200Correct answer

Solution.

Answer: (d) 200200

  1. The function |sin x| has period π and integral 2 over each full period.
  2. Any interval of length 100π covers exactly 100 periods, regardless of its starting point.
  3. Hence φ(a) = 200.