Hey guys,

Can you please show me a step by step integration for

Find the solution for the differential equation :

3Cos^2(x) , y= Pi , x = Pi/2

Thank you !

Printable View

- Apr 14th 2009, 01:47 AMZaZuIntegrate 3cos^2(x)
Hey guys,

Can you please show me a step by step integration for

Find the solution for the differential equation :

3Cos^2(x) , y= Pi , x = Pi/2

Thank you ! - Apr 14th 2009, 02:25 AMmr fantastic
- Apr 14th 2009, 02:42 AMZaZu
Thanks for the reply, but where did the Cos

**2**(x) come from ?! - Apr 14th 2009, 03:04 AMmr fantastic
- Apr 14th 2009, 03:16 AMZaZu
Yes I do, but I dont understand how using that will affect my answer :S

- Apr 14th 2009, 03:24 AMmr fantastic
- Apr 14th 2009, 03:37 AMZaZu
Is it 1/4 Sin2(x) + x ?

- Apr 14th 2009, 03:41 AMmr fantastic
- Apr 14th 2009, 03:44 AMZaZu
Oh sorry didnt realize the 1/2 is multiplied by the whole thing in brackets

So its 1/4 Sin2(x) + x/2 - Apr 14th 2009, 03:47 AMmr fantastic
- Apr 14th 2009, 03:49 AMZaZu
Ohhhh okay got it

So its a rule that I should know, when I have an even power, I should double the angle to get an easier function right ??? - Apr 14th 2009, 04:35 AMShowcase_22
ummm, sort of. You do have to use double angle formulae if that's what you mean.

Think of this:

We already know that (i'll show how Mr F gets his answer since you've never seen it before):

and .

We require an expression for .

from the first identity.

Putting this into the second identity gives:

.

Going back to our original integral:

.

The big problem now is the .

Looking at the integral you posted and what I have done here, can you finish this integral off?

(Hint: and ). - Apr 14th 2009, 04:41 AMZaZu
Thanks, Ill get on with it and ill reply when im done :)