Prove that \(\int\limits_0^{\pi/2}(sin\,x-cos\,x)log(sin\,x+cos\,x)d – InterviewSolution

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1.

Prove that \(\int\limits_0^{\pi/2}(sin\,x-cos\,x)log(sin\,x+cos\,x)dx=0\)∫ (sin x- cos x)log(sin x+ cos x)dx=0, x ∈[0,π/2]

Answer»

Let, sin x + cos x = t

⇒ cos x – sin x dx = dt

At x = 0, t = 1

At x = π/2, t = 1

\(y=\int\limits_0^{1}-logt\,dt\)

We know that when upper and lower limit in definite integral is

equal then value of integration is zero.

So, y = 0

Discussion

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