# Thread: Integrating a trigonometric function.

1. ## Integrating a trigonometric function.

Hi,
Can anyone help me with the following question?

I have to integrate 2sinxcosx Lower limit 0 Upper limit 2

Do I alter 2sinxcosx to sin2x before integrating or do I integrate 2sinxcosx?

Thanks
Cromlix

2. Originally Posted by cromlix
Hi,
Can anyone help me with the following question?

I have to integrate 2sinxcosx Lower limit 0 Upper limit 2

Do I alter 2sinxcosx to sin2x before integrating or do I integrate 2sinxcosx?

Thanks
Cromlix
Dear cromlix,

You could do it both ways.

3. Originally Posted by cromlix
Hi,
Can anyone help me with the following question?

I have to integrate 2sinxcosx Lower limit 0 Upper limit 2

Do I alter 2sinxcosx to sin2x before integrating or do I integrate 2sinxcosx?

Thanks
Cromlix
Either way is fine.

If you convert $\displaystyle 2\sin{x}\cos{x}$ to $\displaystyle \sin{2x}$ you would use a $\displaystyle u$ substitution with $\displaystyle u = 2x$.

If you keep it as $\displaystyle 2\sin{x}\cos{x}$ then you would use a $\displaystyle u$ substitution either with $\displaystyle u = \sin{x}$ or $\displaystyle u = \cos{x}$.