A) \[\frac{\pi }{2}<I<\frac{{{\pi }^{2}}}{4}\]
B) \[\frac{\pi }{4}<I<\frac{{{\pi }^{2}}}{2}\]
C) \[1<I<\frac{\pi }{2}\]
D) \[0<I<1\]
Correct Answer: A
Solution :
[A]Since, \[\sin x\frac{dy}{dx}+y\cos x=1\] |
\[\frac{dy}{dx}+y\cot x=\text{cosec}\,x\] |
IF \[(e=Ns\,\,B\,\,\omega \,\,\sin \,\,\omega t),\] \[y\sin x=\int{\text{cosec}\,x.\,\sin x\,\,dx}\] |
\[y\sin x=x+C\] |
If \[x\to 0,\] y is finite \[\therefore C=O\] |
\[\therefore y=\frac{x}{\sin x}\] |
Now, \[I<\frac{{{\pi }^{2}}}{4}\] and \[I>\frac{\pi }{2}\] |
Hence, \[\frac{\pi }{2}<I<\frac{{{\pi }^{2}}}{4}\] |
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