Integral Calculus Question 352
Question: If $ \frac{d}{dx}f(x)=x\cos x+\sin x $ and $ f(0)=2 $ , then $ f(x)= $
[MP PET 1989]
Options:
A) $ x\sin x $
B) $ x\cos x+\sin x+2 $
C) $ x\sin x+2 $
D) $ x\cos x+2 $
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Answer:
Correct Answer: C
Solution:
$ \frac{d}{dx}f(x)=x\cos x+\sin x $
$ \Rightarrow f(x)=\int_{{}}^{{}}{(x\cos x+\sin x)\ dx}=x\sin x+c $ Since, $ f(0)=2\Rightarrow c=2 $ ;
$ \therefore \ f(x)=x\sin x+2 $ .
BETA
