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Mathematics 17 Online
OpenStudy (konradzuse):

find the definite integral

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)

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

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.:\[\sin(9*\frac{\pi}{9})=\sin(\pi)=0\]

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

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...

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

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

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....

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

OpenStudy (konradzuse):

ROUND 2 http://openstudy.com/study#/updates/4ffb5fe8e4b00c7a70c46834

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