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  4. ∫ limits020 π(| sin x|+| cos x|)2 d x is equal to :-

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Q. $\int\limits_0^{20 \pi}(|\sin x|+|\cos x|)^2 d x$ is equal to :-

JEE MainJEE Main 2022Integrals

Solution:

$ I =\int\limits_0^{20 \pi}(|\sin x |+|\cos x |)^2 dx ;$ ( Jack property)
$ I =40 \int\limits_0^{\pi / 2}(\sin x +\cos x )^2 dx$
$ I =40 \int\limits_0^{\pi / 2}(1+\sin 2 x ) dx $
$ I =20[\pi+2]$