- #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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