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anonymous

  • 4 years ago

Integrate with steps

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  1. anonymous
    • 4 years ago
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    \[\int\limits_{0}^{2\pi} \cos^2 (2\theta) d \theta\]

  2. Zarkon
    • 4 years ago
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    use 1/2 angle formula

  3. anonymous
    • 4 years ago
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    So it becomes \[1/2 + 1/2 \cos (4 \theta)\] ??

  4. anonymous
    • 4 years ago
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    Can we do that?

  5. Zarkon
    • 4 years ago
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    yes

  6. anonymous
    • 4 years ago
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    Okay, thank you.

  7. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    remember it is \[\frac12\int_a^b r^2\,d\theta\] did you include the 1/2?

  9. anonymous
    • 4 years ago
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    Yeah, I forgot that. Ah, just woke up. Thanks.

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