I am not quite sure where you are missing 1/2 but wolfram cnan give you the correct answer
integral theta sin(theta)* (theta cos(theta) ) - Wolfram|Alpha
I am stuck! I've worked and reworked the following integral and I'm off by a factor of 2 (or 1/2) and can't seem to figure out why. Here is my work:
[Applying double-angle identity]
Integrating by parts: letting gives:
Integrating the right hand term:
The text answer is
Where am I missing the other factor of (1/2)??
I am not quite sure where you are missing 1/2 but wolfram cnan give you the correct answer
integral theta sin(theta)* (theta cos(theta) ) - Wolfram|Alpha