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  • The area of the region enclosed by the curve <img alt="\mathrm{f(x)= max\: \: \left \{ sin x, cosx \right \}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%20max%5C%

The area of the region enclosed by the curve \mathrm{f(x)= max\: \: \left \{ sin x, cosx \right \}}, \mathrm{-\pi\leq x\leq \pi} and the x-axis is

Option: 1

2\sqrt{2}\left ( \sqrt{2}+1 \right )


Option: 2

4\left ( \sqrt{2} \right )


Option: 3

4


Option: 4

2\left ( \sqrt{2}+1 \right )


Answers (1)

best_answer

Area = \left|\int_{-\pi}^{\frac{-3 \pi}{4}} \sin x d x\right|+\left|\int_{\frac{-3 \pi}{4}}^{\frac{-\pi}{2}} \cos x d x\right|+\int_{\frac{-\pi}{2}}^{\frac{\pi}{4}} \cos x d x+\int_{\frac{\pi}{4}}^\pi \sin x d x=4

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Anam Khan

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