question_answer

The area bounded by the curves \[y=sinx,\text{ }y=cosx\] and y-axis in I quadrant is -

A) \[\sqrt{2}\]                    

B)        \[\sqrt{2}+1\]

C) \[\sqrt{2}-1\]         

D)        \[\sqrt{2}+2\]

Correct Answer: C

Solution :

[c] Required area \[=\int\limits_{0}^{\pi /4}{\left( cosx-sinx \right)dx}\] \[=(sinx+cosx)_{0}^{\pi /4}\] \[=\left( \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}} \right)-(0+1)=\sqrt{2}-1\]