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

Question 52

Multiple Choice

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


A) 14xcos⁡(4x) −14sin⁡(4x) \frac{1}{4} x \cos (4 x) -\frac{1}{4} \sin (4 x)
B) −14xcos⁡(4x) +14sin⁡(4x) -\frac{1}{4} x \cos (4 x) +\frac{1}{4} \sin (4 x)
C) 14xcos⁡(4x) −116sin⁡(4x) \frac{1}{4} x \cos (4 x) -\frac{1}{16} \sin (4 x)
D) −14xcos⁡(4x) +116sin⁡(4x) -\frac{1}{4} x \cos (4 x) +\frac{1}{16} \sin (4 x)

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