JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region enclosed by the curve \(f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi\) and the \(x\)-axis is
- A \(2(\sqrt{2}+1)\)
- B \(2 \sqrt{2}(\sqrt{2}+1)\)
- C \(4(\sqrt{2})\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
Area \(=\) \(\left|\int \limits_{-\pi}^{\frac{-3 \pi}{4}} \sin x d x\right|+\left|\int \limits_{\frac{-3 \pi}{4}}^{\frac{-\pi}{2}} \cos x d x\right|+\int \limits_{\frac{-\pi}{2}}^{\frac{\pi}{4}} \cos x d x+\int \limits_{\frac{\pi}{4}}^\pi \sin x d x\) \(=4\)
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