## anonymous 4 years ago Integrate with steps

1. anonymous

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

2. Zarkon

use 1/2 angle formula

3. anonymous

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

4. anonymous

Can we do that?

5. Zarkon

yes

6. anonymous

Okay, thank you.

7. anonymous

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

8. Zarkon

remember it is $\frac12\int_a^b r^2\,d\theta$ did you include the 1/2?

9. anonymous

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

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