Need Help With Integration Question (1 Viewer)

[Neon-Frog]

Hey

We've just started the integration topic, so im not really that confident with it all.

This question is really bugging me though.

sin^2(x- pi/4).dx

Any help appreciated
Thanks guys

 

[Lazarus]

Consider using the following transformation:

sin² x = (1/2)(1 - cos 2x) *

e.g.

sin² (x - pi/4) = (1/2)(1 - cos [2x - pi/2])


* can be proved using trig rules.

 

[Neon-Frog]

Thanx alot

I had that, either ive done something wrong in the integration process or the answer is wrong in the back.

Thanks again, i'll have to go back and start from scratch to see what ive done.

 

[KeypadSDM]

Integral = I Sin[x-pi/4]^2dx
but
Sin[x]^2 = (1/2)(1 - Cos[2x])
.'. Integral = I (1/2)(1 - Cos[2x - pi/2])
= (1/4)(2x - Sin[2x-pi/2]) + c