Question

integral of (cos(pi*theta))^2

Answer 1

Hint:


Use the identity


\[\large \cos^2(x) = \frac{1+\cos(2x)}{2}\]

Answer 2

That's what wolframalpha said too, but I'm wondering whether there's another way to do it. I'm pretty weak on identities...

Answer 3

not that I can think of

Answer 4

If you can't remember them, then write them down on a cheat sheet and hopefully your professor will allow you to use one

Answer 5

He's already said that he's not gonna allow a cheat sheet. I thought about quoting Einstein to him, but I don't think it'll help. Guess I'm just going to have to memorize them...

Answer 6

Thanks though.

Answer 7

you're welcome

Answer 8

what was Einsteins quote?

Answer 9

you can also do this problem by parts...but you will need to use \(\sin^2(x)+\cos^2(x)=1\)

Answer 10

Einstein's quote was: "[I do not] carry such information in my mind since it is readily available in books. ...The value of a college education is not the learning of many facts but the training of the mind to think."

Answer 11

(I fully agree.)

Answer 12

Zarkon: how would I do that? Replace 1 with sin^2(x) + cos^2(x)?

Answer 13

Move the 1/2 outside of the integral, split them into three parts, and integrate each one separately?

Answer 14

I really like that quote :)

My philosophy on learning works the same way. Haha.

Answer 15

I like it because I have a bad memory. ;)

Answer 16

\[\cos^2(u)=\cos(u)\cos(u)\]

the use parts

Answer 17

then use \[s^2+c^2=1\]

Answer 18

Okay, thanks.

Answer 19

oh cool nice quote :)

Answer 20

\[\large \int\limits \cos^2(\theta \pi)d \theta\]if we use @jim_thompson5910 's way: let \(x=(\theta \pi)\) \(dx=d(\theta)\)\[\large \int\limits \frac{1+\cos(2(\pi \theta))}{2}d(\theta)\]\[\large \frac{1}{2}\int\limits (1+\cos(2\pi \theta))d(\theta)\] integrate individually. \[\large \frac{1}{2}[\int\limits d(\theta)+\int\limits \cos(2\pi \theta)d(\theta)]\]