A) \[1\]
B) \[\frac{1}{4}\]
C) \[-1\]
D) \[\frac{-1}{4}\]
E) \[-4\]
Correct Answer: B
Solution :
\[\int\limits_{0}^{{{x}^{2}}}{f(t)}dt=x\cos \pi x\] On differentiating both sides, we get \[\therefore \] \[2xf({{x}^{2}})=\frac{-x\sin \pi x}{\pi }+\cos \pi x\] \[\Rightarrow \] \[{{x}^{2}}f{{(x)}^{2}}=-\frac{x\sin \pi x}{{{x}^{2}}\pi }+\frac{\cos \pi x}{{{x}^{2}}}\] \[\therefore \] \[f(4)=f({{2}^{2}})=\frac{1}{4}\]You need to login to perform this action.
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