If \[\int_{\sin x}^{1}{{{t}^{2}}f(t)\ dt=1-\sin x}\],\[x\in \left( 0,\frac{\pi }{2} \right)\] then \[f\ \left( \frac{1}{\sqrt{3}} \right)\] equal to [IIT Screening 2005]

If \[\int_{\sin x}^{1}{{{t}^{2}}f(t)\ dt=1-\sin x}\],\[x\in \left( 0,\

1.	If \[\int_{\sin x}^{1}{{{t}^{2}}f(t)\ dt=1-\sin x}\],\[x\in \left( 0,\frac{\pi }{2} \right)\] then \[f\ \left( \frac{1}{\sqrt{3}} \right)\] equal to [IIT Screening 2005]
A.	3
B.	\[\frac{1}{3}\]
C.	\[\frac{1}{\sqrt{3}}\]
D.	\[\sqrt{3}\]
Answer» B. \[\frac{1}{3}\]

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If \[\int_{\sin x}^{1}{{{t}^{2}}f(t)\ dt=1-\sin x}\],\[x\in \left( 0,\frac{\pi }{2} \right)\] then \[f\ \left( \frac{1}{\sqrt{3}} \right)\] equal to [IIT Screening 2005]

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