what is the integral of xcos(3x) from 0 to pi/2 ?

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what is the integral of xcos(3x) from 0 to pi/2?

Aug 28th, 2015

Thank you for the opportunity to help you with your question!

 ∫xcos(3x)

 = x∫cos3x dx + ∫x* -sin 3x/3 dx

=(3xsin(3x) + cos3x) / 9


now apply the limit from 0 to pi/2

=(3 pi sin(3pi) +cos ( 3 pi) ) /9 - (3*0*sin(3*0) + cos3*0) / 9

= (3 pi *0 + -1 ) /9 - (3*0*0 + 1) / 9

=  -1/9 -1/9

= -2/9


answer is  -2/9



Please let me know if you need any clarification. I'm always happy to answer your questions.....thank you
Aug 28th, 2015

sorry...i thought it was from 0 to pi


the answer for 0 to pi/2

is 

=(3 pi sin(3pi/2) +cos ( 3 pi/2) ) /9 - (3*0*sin(3*0) + cos3*0) / 9

= -pi/6  - 1/9


answer is  -pi/6  - 1/9


please apologize for my mistake......

hope you understood..please message if you have any doubts...thank you


Aug 28th, 2015

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