Q.13 Evaluate : displaystyle∫√(1 + sin 2x)· dx

Answer: sin x - cos x + c 1 + sin 2x = sin² x + cos² x + 2sin xcos x = (sin x + cos x)² . therefore displaystyle∫√(1 + sin 2x) dx = ∫(sin x + cos x) dx = -cos x + sin x + c .

Evaluate : \(\displaystyle\int\sqrt{1 + \sin 2x}\cdot dx\)

Q.13 Evaluate : \(\displaystyle\int\sqrt{1 + \sin 2x}\cdot dx\)

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: \(\sin x - \cos x + c\)

\(1 + \sin 2x = \sin^2 x + \cos^2 x + 2\sin x\cos x = (\sin x + \cos x)^2\).

\(\therefore \displaystyle\int\sqrt{1 + \sin 2x}\,dx = \int(\sin x + \cos x)\,dx = -\cos x + \sin x + c\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Evaluate : \(\displaystyle\int\sqrt{1 + \sin 2x}\cdot dx\)

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