The area of the region that lies inside both curves r² = 2sin(2θ), r = 1 is -0.1287 square units.
<h3>How to find the area of the region that lies inside both curves?</h3>
Since the curves are
We find their point of intersection.
So, r² = r²
2sin(2θ) = 1²
2sin(2θ) = 1
sin(2θ) = 1/2
2θ = sin⁻¹(1/2)
2θ = π/6
θ = π/12
So, we integrate the area from θ = 0 to θ = π/12
Now the area A of the region between two curves between θ = α to θ = β is
So, the area betwwen the curves r² = 2sin(2θ), r = 1 between θ = 0 to θ = π/12 is
So, the area of the region that lies inside both curves r² = 2sin(2θ), r = 1 is -0.1287 square units.
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