Question

If $\frac{d}{dx}f(x) = x\cos x + \sin x$ and $f(0) = 2,$ then $f(x) =$

• A. $x\sin x$
• B. $x\cos x + \sin x + 2$
• C. $x\sin x + 2$
• D. $x\cos x + 2$

Answer 1

Answer: (C)

$x\sin x + 2$

Answer 2

$\frac{d}{dx}f(x) = x\cos x + \sin x \Rightarrow f(x) = \int_{}^{}{(x\cos x + \sin x)dx} = x\sin x + c$Since $f(0) = 2$

$\Rightarrow c = 2$, $\therefore f(x) = x\sin x + 2$