Evaluate 0/4 x\,3x\,dx.

GATE 2024 MN – Question 16

Engineering Mathematics · Calculus · 1 mark · Multiple choice

Evaluate $\int_0^{\pi/4}\cos x\,\sin^3x\,dx$.

Show answer and explanation

Correct answer: (B) 1/16

Set u=sin x, so du=cos x dx. The antiderivative is sin⁴x/4. At π/4, sin⁴x=1/4, while at zero it is 0. Thus the integral is 1/16, B.

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