Question

Find area bounded by the curves \(y\) = \(max\{sin x, cos x\}\) and \(x-axis\) between \(x = -  \pi  \)and \(x =   \pi\)

• A. \(2 + \sqrt{2}\)
• B. \(\sqrt{2}\)
• C. \(1 + \sqrt{2}\)
• D. \(2\sqrt{2}\)

Answer 1

The Correct Option is D

 

\(\int_{-\pi}^{-3\frac{\pi}{4}}sinx\,dx+\int_{-3\frac{\pi}{4}}^{\frac{\pi}{4}}cosx\,dx+\int_{\frac{\pi}{4}}^{\pi}sinx\,dx\)

\(-cos\,x|^{-3\frac{\pi}{4}}_{-\pi}+sin\,x|^{\frac{\pi}{4}}_{-3\frac{\pi}{4}}+ \,-cos\,x|^{\pi}_{\frac{\pi}{4}}\)

\(=(\frac{1}{\sqrt2}-1)+(\frac{1}{\sqrt2}+\frac{1}{\sqrt2})+(1+\frac{1}{\sqrt2})\)

\(=2\sqrt2\)

The correct option is (D): \(2\sqrt{2}\)