Question

Calculate the following integral \[\int\limits_{0}^{\pi/2} \sin3\theta \cos \theta dx \]

Answer 1

\[ sin 3xcosx = \frac{1}{2} (sin(3x-x) + sin(3x+x) \]
\[\frac{1}{2} sin(2x) + sin(4x)\]

Answer 2

I used \(x\) instead of \(\theta\) cos it's easier to type.

Answer 3

\[ \frac{1}{2}\int sin(2x) + \int sin(4x)\]

Answer 4

\[ = \frac{1}{2} * -\frac{1}{2} cos(2x) + -\frac{1}{4}sin(4x) +c\]

Answer 5

don't forget to sub in the limit.

Answer 6

Thank you, it gives me the right answer