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GATE 2014 CS (CS3) – Question 57

Engineering Mathematics · Calculus · 2 marks · Multiple choice

Evaluate $\int_0^\pi x^2\cos x\,dx$.

  1. $-2\pi$
  2. $\pi$
  3. $-\pi$
  4. $2\pi$

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Correct answer: (A) $-2\pi$

Explanation

Integration by parts gives[x²sinx]₀^π−2∫₀^πxsinx dx. The boundary term vanishes, and the remaining integral isπ. Therefore the value is **−2π,A**. A second integration by parts confirms the sign.