Question

Use an appropriate method to evaluate each of the following definite integrals

Lower limit: pi/4
Upper Limit: pi /2
Integral: xcos(3x)dx

Use an appropriate method to evaluate each of the following definite integrals

Lower limit: pi/4
Upper Limit: pi /2
Integral: xcos(3x)dx

@Mathematics

Answer 1

can we do integration by parts

Answer 2

Yes

Answer 3

Please is you can show the steps I will greatly appreciate it, thank you kindly

Answer 4

\[\int\limits_{\pi/4}^{\pi/2}xcos(x)dx = xsinx|_{\pi/4}^{\pi/2} - \int\limits_{\pi/4}^{\pi/2}\sin(x)dx = (xsin(x)+\cos(x))|_{\pi/4}^{\pi/2}\]
Here I set u=x => du=dx and dv=cos(x)dx => v=sinx

Answer 5

@kietjohn ok, so I am not suppose to end up with a numerical value?

Answer 6

plug in upper limit then minus (plug in lower limit)

Answer 7

Thank you

Answer 8

So Kietjohn set up is correct?

Answer 9

looks good to me

Answer 10

K thanks

Answer 11

I thought the dv should be cos(3x)

Answer 12

yeah he did for cos(x) not cos(3x)