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NDA 2025 Maths · Mathematics · Definite Integrals · medium

Evaluate the integral of the modulus function: ∫0^π|cos x| dx

Single correct option

Evaluate the integral of the modulus function: ∫0π∣cos⁡x∣ dx\displaystyle\int_0^{\pi}|\cos x|\,dx
  1. A. 00
  2. B. 11
  3. C. π\pi
  4. D. 22
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Answer: (D) 22

cos⁡x≥0\cos x\ge0 on [0,π2][0,\frac\pi2] and ≤0\le0 on [π2,π][\frac\pi2,\pi]. So the integral is ∫0π/2cos⁡x dx+∫π/2π(−cos⁡x)dx=1+1=2\int_0^{\pi/2}\cos x\,dx+\int_{\pi/2}^\pi(-\cos x)dx=1+1=2. Without the modulus the integral is 00; the value 11 counts only one half.
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Original question written in the NDA 2025 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