Question

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

• A. x sin x
• B. x cosx + sinx + 2
• C. x sinx + 2
• D. x cosx + 2

Answer 1

Answer: (C)

x sinx + 2

Answer 2

Integrating both sides :

$\int \frac { \mathrm { d } } { \mathrm { dx } }$ f(x) =$\int_{}^{}{x\cos xdx + \int_{}^{}{\sin xdx}}$

f(x) = x$\int_{}^{}{\cos xdx}$–$\int_{}^{}\left( 1.\int_{}^{}{\cos xdx} \right)$ dx + $\int_{}^{}{\sin xdx}$

f(x) = x sinx – $\int_{}^{}{\sin x}$dx + $\int_{}^{}{\sin x}$dx

f(x) = x sin x + c Ž f(0) + 2

2 = 0 + c Ž \ c = 2 Ž \ f(x) = x sin x + 2