Quick question - Faster integration methods for [sin^2 (ax)] WITHOUT substitution? (1 Viewer)

[blackops23]

Hi guys, I was wondering whether there was a way to integrate functions in the form of (sin ax)^2 or (cos ax)^2 without using the substitution of u=ax.

Not too sure on this but I think it is something using double angle formulas e.g. to integrate cos^2 x... you change it to (cos2x +1)/2.

Is there some way of doing it for the form of sin^2 ax or cos^2 ax where a is not equal to one?

Thank you very much, appreciate the help

 

[funnytomato]

Re: Quick question - Faster integration methods for [sin^2 (ax)] WITHOUT substitutio

Hi guys, I was wondering whether there was a way to integrate functions in the form of (sin ax)^2 or (cos ax)^2 without using the substitution of u=ax.

Not too sure on this but I think it is something using double angle formulas e.g. to integrate cos^2 x... you change it to (cos2x +1)/2.

Is there some way of doing it for the form of sin^2 ax or cos^2 ax where a is not equal to one?

Thank you very much, appreciate the help

LOL, didn't u just answer yourself ?

e.g. to integrate cos^2 x... you change it to (cos2x +1)/2
and to integrate cos^2 ax... you change it to (cos2ax +1)/2

 

[AAEldar]

Re: Quick question - Faster integration methods for [sin^2 (ax)] WITHOUT substitutio



Similarly for sine.

 

[blackops23]

Re: Quick question - Faster integration methods for [sin^2 (ax)] WITHOUT substitutio

LOL, didn't u just answer yourself ?

e.g. to integrate cos^2 x... you change it to (cos2x +1)/2
and to integrate cos^2 ax... you change it to (cos2ax +1)/2

ahhh i see, thanks