A) \[\frac{1}{\sqrt{2}}+1\]
B) \[1-\frac{1}{\sqrt{2}}\]
C) \[\frac{\pi }{4\sqrt{2}}\]
D) \[\frac{\pi }{4\sqrt{2}}+\frac{1}{\sqrt{2}}-1\]
Correct Answer: D
Solution :
Required area = Area of rectangle \[OABC\]-Area of curve OABO \[=\frac{\pi }{4}\times \frac{1}{\sqrt{2}}-\int_{0}^{\pi /4}{\sin \text{y dy}}\] \[=\frac{\pi }{4\sqrt{2}}+[\cos y]_{0}^{\pi /4}\] \[=\frac{\pi }{4\sqrt{2}}+\cos \frac{\pi }{4}-\cos 0\] \[=\frac{\pi }{4\sqrt{2}}+\frac{1}{\sqrt{2}}-1\]You need to login to perform this action.
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