Integration cosine function

[johnbobson]

Hello. This is only my third post and I hope I am allowed to post problems in links. Is there a way to type math symbols on this forum?

I would appreciate it if someone could solve the following problem step by step.

http://imageshack.us/photo/my-images/24/problem4b.jpg/

Note: It is not arccos, A is a constant.

My work:


∫[-T/2, T/2] A² (cos (2 * π * f₀ * t + Φ))² dt = ∫[-T/2, T/2] A² cos²(2 * π * f₀ * t + Φ) dt = A² ∫[-T/2, T/2] cos²(2 * π * f₀ * t + Φ) dt = I am stuck here and do not know how to continue

Can someone please show the next few steps?

 

[Deleted member 4993]

Hello. This is only my third post and I hope I am allowed to post problems in links. Is there a way to type math symbols on this forum?

I would appreciate it if someone could solve the following problem step by step.

Note: It is not arccos, A is a constant.

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[johnbobson]

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

Can you help me now?

 

[Deleted member 4993]

Hello. This is only my third post and I hope I am allowed to post problems in links. Is there a way to type math symbols on this forum?

I would appreciate it if someone could solve the following problem step by step.

http://imageshack.us/photo/my-images/24/problem4b.jpg/

Note: It is not arccos, A is a constant.

My work:


∫[-T/2, T/2] A² (cos (2 * π * f₀ * t + Φ))² dt = ∫[-T/2, T/2] A² cos²(2 * π * f₀ * t + Φ) dt = A² ∫[-T/2, T/2] cos²(2 * π * f₀ * t + Φ) dt = I am stuck here and do not know how to continue

Can someone please show the next few steps?

substitute:

Θ = 2 * π * f₀ * t + Φ

and use:

cos²(α) = {1 + cos(2α)}/2

make sure you change the limits accordingly, and continue...