Calculate the area of one petal of r = 2cos(3θ)?

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Calculate the area of one petal of r = 2cos(3θ)?

2007-04-18 17:56:28 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

∫(1/2)r² dθ

= 2∫(1/2)[2cos(3θ)]² dθ

= 4∫cos²(3θ) dθ

= 2∫[1 + cos(6θ)] dθ | [Evaluated from 0 to π/6]

= 2[θ + sin(6θ)/6] | [Evaluated from 0 to π/6]

= 2π/6 = π/3

2007-04-18 19:29:13 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋

you first.

2007-04-19 00:58:59 · answer #2 · answered by Anonymous · 0⤊ 1⤋