question_answer

The area formed by triangular shaped region bounded by the curves \[y=\sin x,y=\cos x\]and \[x=0\]is

A)  \[(\sqrt{2}-1)sq\,unit\]      

B)         \[\text{1}\,\text{sq}\,\text{unit}\]                   

C)         \[\sqrt{\text{2}}\,\text{sq}\,\text{units}\]                      

D)         \[(\sqrt{2}+1)\,sq\,unit\]

Correct Answer: A

Solution :

Area \[=\int_{0}^{\pi /4}{(\cos x-\sin x)}dx=(\sqrt{2}-1)sq\]        unit \[(\because \,y=\sin \,x\,and\,y=\cos x\,meet\,x=\pi /4)\]