How do you intergrate cos^3 [x] .dx

[suddy72]

could some one please show me the steps to doing this ??

 

[HallsofIvy]

$\int cos^3(x)dx$ is a standard problem. Anytime you have an odd power of either sin or cos take one of the out to match with the dx:

$$\int(cos^2(x))(cos(x)dx)$$

Now we can use $sin^2(x)+ cos^2(x)= 1$ to convert to the other trig function:

$$\int(1- sin^2(x))(cos(x)dx)$$

and, of course, the whole reason for taking out that orginal "cos(x)" is that
d(sin(x))= cos(x)dx.

Let u= sin(x). Then du= cos(x)dx and the integral is

$$\int(1-u^2)du$$
and that should be easy.

 

[Xishan]

Well, I beg your forgiveness for this question b/c its really an irrelevant one.

Can you please tell me how you use these mathematical symbols like integral sign and superscripts etc in your messages?

 

[deltabourne]

Well, I beg your forgiveness for this question b/c its really an irrelevant one.

Can you please tell me how you use these mathematical symbols like integral sign and superscripts etc in your messages?

It's called LaTex Math Typesetting and is really pretty cool. Check out this thread for more information:
https://www.physicsforums.com/showthread.php?t=8997

 

[Theelectricchild]

suddy, if you want a place to check your work, the integrator works fine--- powered by mathematica.

http://integrals.com/