Mathematics
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OpenStudy (konradzuse):
find the definite integral
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OpenStudy (konradzuse):
\[\int\limits_{0}^{\pi/9} xcos(9x)dx\]
OpenStudy (konradzuse):
u = x
du = dx
dv = cos(9x)dx
1/9 sin(9x)
OpenStudy (konradzuse):
\[\frac{x}{9}\sin(9x) - \frac{1}{9}\int\limits \sin(9x)dx\]
OpenStudy (konradzuse):
\[\frac{x}{9}\sin(9x) - \frac{1}{9} -\cos(9x)+c\]
OpenStudy (konradzuse):
acutally it should be 1/9cos(9x)
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OpenStudy (anonymous):
almost,
\[\frac{x}{9}sin(9x)-\frac{1}{9} \int sin(9x) \]
Or did you think about something else? (This is only the first step)
OpenStudy (konradzuse):
same thing i got, now to do the next step.
OpenStudy (asnaseer):
you missed multiplying by the 1/9 outside the integral, so it should be:\[\frac{x}{9}\sin(9x) + \frac{1}{81}\cos(9x)+c\]
OpenStudy (konradzuse):
yup I said I forgot the 1/9 :P
OpenStudy (konradzuse):
so since this is a definite integral from 0 to pi/9
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OpenStudy (konradzuse):
\[[\frac{\frac{\pi}{9}}{9}\sin(9*\frac{\pi}{9}) +\frac{1}{81}\cos(9 * \frac{\pi}{9})] - [\frac{0}{9}\sin(9*0) +\frac{1}{81}\cos(9 * 0)]\]
OpenStudy (konradzuse):
\[[\frac{\frac{\pi}{9}}{9}\sin(9*\frac{\pi}{9}) +\frac{1}{81}\cos(9 * \frac{\pi}{9})] - [\frac{1}{81}]\]
OpenStudy (asnaseer):
cancel the 9's in the sin/cos
OpenStudy (asnaseer):
and then simplify further
OpenStudy (asnaseer):
e.g.:\[\sin(9*\frac{\pi}{9})=\sin(\pi)=0\]
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OpenStudy (asnaseer):
do you understand?
OpenStudy (konradzuse):
yessir.
OpenStudy (asnaseer):
so what final answer do you get?
OpenStudy (konradzuse):
what shall I do with pi/9/9
OpenStudy (asnaseer):
ignore it because it is multiplied by zero
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OpenStudy (konradzuse):
I guess nothing since sin(pi) = 0 so it's just 0...
OpenStudy (konradzuse):
so it's -1/81 - 1/81 so 1/162?
OpenStudy (asnaseer):
not quite
OpenStudy (konradzuse):
oh wait 0?
OpenStudy (asnaseer):
no...
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OpenStudy (konradzuse):
nvm lol
OpenStudy (asnaseer):
:)
OpenStudy (konradzuse):
cos(pi) is -1
OpenStudy (konradzuse):
sorry my head is about to kerplode.
OpenStudy (asnaseer):
better wear a crash helmet then :D
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OpenStudy (konradzuse):
:)
OpenStudy (konradzuse):
so it's not -1/162?
OpenStudy (asnaseer):
\[-\frac{1}{81}-\frac{1}{81}=-\frac{2}{81}\]
OpenStudy (konradzuse):
oh.
OpenStudy (konradzuse):
derp :P
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OpenStudy (asnaseer):
I think you were trying to multiply them
OpenStudy (konradzuse):
yeah Idk I cannot compute anything anymore LOL
OpenStudy (asnaseer):
or something?
OpenStudy (asnaseer):
maybe you need a rest - too much math is not good for your health :)
OpenStudy (konradzuse):
I know... I need to get this done by midnight soo....
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OpenStudy (konradzuse):
gotta smash through it...
OpenStudy (asnaseer):
you certainly are persistent - that is a good quality - I'm sure you will go far in life :)
OpenStudy (konradzuse):
I hope :p