cos^3 x (1 Viewer)

[747nick]

Hello,


I'm tryingto figure out the integral of cos^3 x...and I cant get past the first step!

Could somebody please point me in the right direction after:

(1 + cos 2x) cos x dx

Thanks so much for your help in advance

 

[SoulSearcher]

cos³x
= cos x * cos²x
= cos x (1 - sin²x)
= cos x - sin²x * cos x

That can be integrated easily now.

 

[747nick]

Thanks so much!

 

[crazysambo]

hey guys im not tryin to b rude or nuthin, but lik the trials r lik 1 week left with maths next week and u cant do this, lik seriously do u really try at ext 1 maths. i do ext 1 maths and im ranked 47/49 but since ive been studying for trials im able to answer 90% of teh q's the teacher has been puttin up over the last week. lik just think about it

 

[Forbidden.]

cos³x
= cos x * cos²x
= cos x (1 - sin²x)
= cos x - sin²x * cos x

That can be integrated easily now.

uh oh ... I think I got sin³x in my 3u maths trial paper and i changed it to (sin x)³ in order to solve it

 

[Slidey]

sin^3(x) and (sinx)^3 are exactly the same thing, silly.

Another solution is integration by parts:

Int cos^3(x) dx = Int cos^2(x).(sinx)' dx

 

[2syllables]

sin^3(x) and (sinx)^3 are exactly the same thing, silly.

Another solution is integration by parts:

Int cos^3(x) dx = Int cos^2(x).(sinx)' dx

mate there are people who dont do 4 unit

 

[SoulSearcher]

mate there are people who dont do 4 unit

All he was doing is pointing out another way to evaluate the integral. If you're not doing extension 2, then ignore it.

 

[2syllables]

All he was doing is pointing out another way to evaluate the integral. If you're not doing extension 2, then ignore it.

wise words from a wise old man lol

 

[SoulSearcher]

wise words from a wise old man lol

Shut up young'un