The area of the small loop of the lemniscate defined by the equation r = 1 + 2sin(2θ) can be calculated using the integral formula A = 0.5 ∫[f(θ)]² dθ. To determine the limits of integration, one must identify the maxima and minima of the curve within the interval [0, 2π]. The values of θ where f(θ) = 0, which occur before and after the minima, establish the necessary limits for the integral calculation.
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