A) \[-1\]
B) \[0\]
C) \[1\]
D) \[2\]
Correct Answer: C
Solution :
[c] \[f(x)=\sin x-\int\limits_{0}^{x}{(x-t)f(t)dt}\] \[=\sin x-x\int\limits_{0}^{x}{f(t)\,dt+}\int\limits_{0}^{x}{tf\,(t)\,dt}\] \[\therefore \,\,\,f'(x)=\cos x-xf(x)-\int\limits_{0}^{x}{f(t)\,dt+xf(x)}\] \[=\cos x-\int\limits_{0}^{x}{f(t)dt}\] \[\therefore \,\,\,g'(0)=1\]You need to login to perform this action.
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