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The curves are r = 7sin(2θ) and r = 7sin(θ)

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First we find out the point where the two curves intersect.So equate the the two curve.

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7sin(2θ) = 7sin(θ)

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2sinθ cosθ = sinθ

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2cosθ = 1

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cosθ = 1/2

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θ = π/3.

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Graph:

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Draw the graph in polar - cordinate plane

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We can observe from the graph that the two curves intersect at θ = π/3 line.

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Now first we find the area of the bounded region in first then we double it for the total area.

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The bounded region is divide into two region(as highligted in the graph)

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One of the region, the θ varies from 0 to π/3 and the curve is r = 7sin(θ)

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Second region, the θ varies from π/3 to π/2 and the curve is r = 7sin(2θ)

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Area of the bounded is given by

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We know that and 

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Therefore area of the bounded region is .

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