What is $F (x) = \int sin (3 x) - sin x {cos}^{2} (4 x) d x$ $F(x) = int sin(3x)-sinxcos^2(4x) dx$ if $F (π) = 3$ $F(pi) = 3$ ?

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What is $F (x) = \int sin (3 x) - sin x {cos}^{2} (4 x) d x$ $F(x) = int sin(3x)-sinxcos^2(4x) dx$ if $F (π) = 3$ $F(pi) = 3$ ?

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Answer 1 · 2017-04-28T22:16:56

$F (x) = \frac{1}{2} cos x - \frac{1}{3} cos 3 x - \frac{1}{28} cos 7 x + \frac{1}{36} cos 9 x + \frac{199}{63}$ $F(x) =1/2cosx-1/3cos3x-1/28cos7x+1/36cos9x+199/63$

Explanation:

$F (x) = \int sin 3 x - sin x {cos}^{2} (4 x) d x =$ $F(x) = int sin3x - sinxcos^2(4x)dx=$
$\frac{1}{2} cos x - \frac{1}{3} cos 3 x - \frac{1}{28} cos 7 x + \frac{1}{36} cos 9 x + c$ $1/2cosx-1/3cos3x-1/28cos7x+1/36cos9x+"c"$

$F (π) = - \frac{10}{63} + c = 3$ $F(pi)= -10/63 + "c"=3$

$c = \frac{199}{63}$ $"c"=199/63$

$F (x) = \frac{1}{2} cos x - \frac{1}{3} cos 3 x - \frac{1}{28} cos 7 x + \frac{1}{36} cos 9 x + \frac{199}{63}$ $F(x) =1/2cosx-1/3cos3x-1/28cos7x+1/36cos9x+199/63$

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What is $F (x) = \int sin (3 x) - sin x {cos}^{2} (4 x) d x$ $F(x) = int sin(3x)-sinxcos^2(4x) dx$ if $F (π) = 3$ $F(pi) = 3$ ?

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What is F(x) = int sin(3x)-sinxcos^2(4x) dxF(x)=∫sin(3x)−sinxcos2(4x)dxF(x) = int sin(3x)-sinxcos^2(4x) dx if F(pi) = 3 F(π)=3F(pi) = 3 ?

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What is $F (x) = \int sin (3 x) - sin x {cos}^{2} (4 x) d x$ $F(x) = int sin(3x)-sinxcos^2(4x) dx$ if $F (π) = 3$ $F(pi) = 3$ ?