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) \(-\frac{1}{4} x \cos (4 x)+\frac{1}{16} \sin (4 x)\)

---

Definitions:

Neologism

A newly coined word or expression that may be in the process of entering common use.

Avolition

Refers to a decrease in the motivation to initiate and perform self-directed purposeful activities.

Auditory

Pertaining to the sense or organs of hearing, or to the process of perceiving sound.

Visual

Pertaining to the sense of sight or the perception of objects through light signals received and processed by the eyes.