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← JEE Main 2017 · 2 Apr · Shift 1
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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 75

The integral ∫π/43π/4dx1+cos⁡x\displaystyle\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos x} is equal to :

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Answer and worked solution

Official answer: A

∫dx1+cos⁡x=tan⁡x2\displaystyle\int\frac{dx}{1+\cos x}=\tan\frac x2, so the integral is tan⁡3π8−tan⁡π8=(2+1)−(2−1)=2\tan\frac{3\pi}8-\tan\frac\pi8=(\sqrt2+1)-(\sqrt2-1)=2.

Topics:Fundamental theorem of calculus
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