A) Area bounded by curve \[y=\frac{1}{1+{{x}^{2}}}\] and \[y=0\] is \[\frac{\pi }{2}\]
B) Area bounded by \[{{c}_{1}}\] and \[{{c}_{2}}\] is \[\frac{\pi }{2}-1\]
C) Area bounded by \[{{c}_{1}}\] and \[{{c}_{2}}\] is \[1-\frac{\pi }{2}\]
D) Area bounded by curve \[y=\frac{1}{1+{{x}^{2}}}\] and x-axis is \[\frac{\pi }{2}\]
Correct Answer: B
Solution :
[b] Area bounded by \[y=\frac{1}{1+{{x}^{2}}}\] and x - axis is \[\int_{-\infty }^{\infty }{\frac{1}{1+{{x}^{2}}}dx=\pi }\] Area bounded by two curves is \[\int_{-1}^{1}{\left( \frac{1}{1+{{x}^{2}}}-\frac{{{x}^{2}}}{2} \right)dx=\frac{\pi }{2}-1}\]You need to login to perform this action.
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