Express the region inside the leaf of the rose r=2sin2θ in the first quadrant as an iterated integral over R
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Express the region inside the leaf of the rose r=2sin2θ in the first quadrant as an iterated integral over R

[From: ] [author: ] [Date: 11-04-30] [Hit: ]
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The leaf in the first quadrant touches r = 0 when 2 sin(2θ) = 0
==> 2θ = 0, π ==> θ = 0, π/2.

Hence, the area of this leaf equals ∫∫ 1 dA
= ∫(θ = 0 to π/2) ∫(r = 0 to 2 sin(2θ)) 1 * (r dr dθ).

I hope this helps!
1
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