A) \[\frac{5}{2}\]
B) \[5\]
C) \[\frac{2}{5}\]
D) \[2\]
Correct Answer: A
Solution :
Given, \[F(x)=\int_{0}^{x}{f(t)\,\,dt}\] \[\therefore \] \[F{{(x)}^{2}}=\int_{0}^{{{x}^{2}}}{f(t)\,\,dt}\] \[\Rightarrow \] \[{{x}^{2}}(1+x)=\int_{0}^{{{x}^{2}}}{f(t)\,dt}\] On differentiating w. r. t. x on both sides by Leibnitz rule, \[2x+3{{x}^{2}}=f{{(x)}^{2}}.2x\] Put \[x=1,\] \[2+3=f(1).2\] \[\Rightarrow \] \[f(1)=\frac{5}{2}\]You need to login to perform this action.
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