- #1
johnhuntsman
- 76
- 0
r = sin 2θ, r = cos 2θ.
I'm having some trouble setting this up.
$$1/2 \int_{\ -pi/8}^{\pi/8} cos^2 2θ~d\theta - 1/2 \int_{\ -pi/8}^{\pi/8} sin^2 2θ~d\theta $$
Which can be:
$$\int_0^{\pi/8} cos^2 2θ~d\theta - \int_0^{\pi/8} sin^2 2θ~d\theta $$
Since there are 8 petals.
$$8 \int_0^{\pi/8} cos^2 2θ~d\theta - 8 \int_0^{\pi/8} sin^2 2θ~d\theta $$
Which becomes:
____(π / 8)
[2sin 4θ]
______0
Which gives me the wrong answer. Somehow the answer is (π / 2) - 1. Can someone please tell me what's wrong with the way I set it up?
I'm having some trouble setting this up.
$$1/2 \int_{\ -pi/8}^{\pi/8} cos^2 2θ~d\theta - 1/2 \int_{\ -pi/8}^{\pi/8} sin^2 2θ~d\theta $$
Which can be:
$$\int_0^{\pi/8} cos^2 2θ~d\theta - \int_0^{\pi/8} sin^2 2θ~d\theta $$
Since there are 8 petals.
$$8 \int_0^{\pi/8} cos^2 2θ~d\theta - 8 \int_0^{\pi/8} sin^2 2θ~d\theta $$
Which becomes:
____(π / 8)
[2sin 4θ]
______0
Which gives me the wrong answer. Somehow the answer is (π / 2) - 1. Can someone please tell me what's wrong with the way I set it up?
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