For $f(x)=x \sin (4 x)$ , Find a Function $F(x)$ Such That $F^{\prime}(x)=f(x)$

question 52

Multiple Choice

For $f(x) =x \sin (4 x)$ , find a function $F(x)$ such that $F^{\prime}(x) =f(x)$ and $F(0) =0$ .

• A) \(\frac{1}{4} x \cos (4 x)-\frac{1}{4} \sin (4 x)\)
• B) \(-\frac{1}{4} x \cos (4 x)+\frac{1}{4} \sin (4 x)\)
• C) \(\frac{1}{4} x \cos (4 x)-\frac{1}{16} \sin (4 x)\)
• D) \(-\frac{1}{4} x \cos (4 x)+\frac{1}{16} \sin (4 x)\)

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