# Thread: Integrating a trigonometric function!?

1. ## Integrating a trigonometric function!?

Trying to integrate fx = (xsin3x) with the limits upper limit=pi/3 and lower limit 0.

I tried integration by parts but doesnt seem to work out.

u=x so du= 1
dv=sin3x so v=-cos3x

then i tried (uv- /int vdu)

now im still stuck... answers or help would be much appreciated

2. Originally Posted by Yehia
Trying to integrate fx = (xsin3x) with the limits upper limit=pi/3 and lower limit 0.

I tried integration by parts but doesnt seem to work out.

u=x so du= 1
dv=sin3x so v=-cos3x

then i tried (uv- /int vdu)

now im still stuck... answers or help would be much appreciated
That's exactly what you do... except if $\displaystyle dv = \sin{3x}$ then $\displaystyle v = -\frac{1}{3}\cos{3x}$.

So $\displaystyle \int{x\sin{3x}\,dx} = -x\cos{3x} - \int{-\cos{3x}\cdot 1\,dx}$

$\displaystyle = -x\cos{3x} + \int{\cos{3x}\,dx}$

$\displaystyle = -x\cos{3x} + \frac{1}{3}\sin{3x} + C$.
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