$\mathop \smallint \nolimits_0^{\pi /4} \,\,(\cos \,\,x\,\, - \,\,\sin x) + \mathop \smallint \nolimits_{\pi /4}^{5\pi /4} (\sin \,\,x\,\, - \,\,\cos \,\,x)\,\,dx\,\, + \,\,\mathop \smallint \nolimits_{2\pi }^{\pi /4} \,\,(\cos \,\,x\,\, - \,\,\sin \,\,x)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_0^{\pi /4} \,\,(\cos \,\,x\,\, - \,\,\sin x) + \int \nolimits_{\pi /4}^{5\pi /4} (\sin \,\,x\,\, - \,\,\cos \,\,x)\,\,dx\,\, + \,\,\int \nolimits_{2\pi }^{\pi /4} \,\,(\cos \,\,x\,\, - \,\,\sin \,\,x)\,\,dx

is equal to

View answer and explanation

Correct option: D

4\,\sqrt 2 - 2

Option D (

4\sqrt 2 - 2

) is correct because after evaluating each integral and summing the results, the final value is

4\sqrt{2} - 2

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