Integrate (cosx)^3 (1 Viewer)

[akukei]

How do you integrate (cosx)^3?

Thanks =]

 

[tommykins]

int cos^3 x = int cosx.(1-sin^2 x) = int cosx - cosxsin^2 x = sinx - (sin^3 x)/3 + c

 

[conics2008]

You Know That Cos^2(x) = 1-sin^2(x) Right ?

Therefore Cos^3(x) = (1-sin^2(x))cos(x)

Expand That

You Get Cos(x)-sin^2(x)cos(x)

Now Integrate By Terms..

You Get Sin(x)-1/3(sin^3(x))

Because If You Look At The Pattern F(x) = Sin(x) And F'(x)=cos(x)

So It Would Make Sense That 1/3sin^3(x) Is The Integral =) Good Luck !

 

[akukei]

Yeah thanks =]

The MIF book had some really strange answer so they are obviously wrong or did it some other way...

thanks to both of you

 

[tommykins]

Yeah thanks =]

The MIF book had some really strange answer so they are obviously wrong or did it some other way...

thanks to both of you

Yes I tried doing that question on the train and the answer just tripped me out.

4unit way is alot simpler though