Question

Integrate with steps

Answer 1

\[\int\limits_{0}^{2\pi} \cos^2 (2\theta) d \theta\]

Answer 2

use 1/2 angle formula

Answer 3

So it becomes \[1/2 + 1/2 \cos (4 \theta)\] ??

Answer 4

Can we do that?

Answer 5

yes

Answer 6

Okay, thank you.

Answer 7

Um... Something's wrong with what I'm doing. The original question is to find the area of one of the clovers of \[r = \cos2 \theta\] So I did the integration of 0 to 2pi of the equation squared. I then divided by 1/4 to get 1 clover. But I got pi/4 instead of the answer pi/8

Answer 8

remember it is \[\frac12\int_a^b r^2\,d\theta\]

did you include the 1/2?

Answer 9

Yeah, I forgot that. Ah, just woke up. Thanks.