A) \[4\sqrt{2}-1\]
B) \[4\sqrt{2}+1\]
C) \[4\sqrt{2}-2\]
D) \[4\sqrt{2}+2\]
Correct Answer: C
Solution :
Required area A is given by \[A=\int_{0}^{3\pi /2}{|\cos x-\sin x|}dx\] \[\Rightarrow \]\[A=\int_{0}^{\pi /4}{|\cos x-\sin x|}dx+\] \[\int_{\pi /4}^{5\pi /4}{|\cos x-\sin x|dx+}\]\[\int_{5\pi /4}^{3\pi /2}{|\cos x-\sin x|dx}\] \[\Rightarrow \] \[A=\int_{0}^{\pi }{(\cos \,x-\sin x)dx+}\] \[\int_{\pi /4}^{5\pi /4}{(\sin x-\cos x)dx+}\] \[\int_{5\pi /4}^{3\pi /2}{(\cos x-\sin x)dx}\] \[\Rightarrow \] \[[\sin x+\cos x]_{0}^{\pi /4}+[-\cos x-\sin x]_{\pi /4}^{5\pi /4}\] \[+[\sin x+\cos x]_{5\pi /4}^{3\pi /2}\] \[\Rightarrow \]\[A=(\sqrt{2}-1)+(\sqrt{2}+\sqrt{2})+(-1+\sqrt{2})\] \[\Rightarrow \]\[A=4\sqrt{2}-2\]You need to login to perform this action.
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