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

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

anonymous · Answer

can we do integration by parts

anonymous · Answer

Yes

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

myininaya · Answer

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

anonymous · Answer

Thank you

anonymous · Answer

So Kietjohn set up is correct?

myininaya · Answer

looks good to me

anonymous · Answer

K thanks

anonymous · Answer

I thought the dv should be cos(3x)

myininaya · Answer

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