The curves and enclose a bounded region for

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The curves r=3+2cos⁡θr = 3 + 2\cos\theta and r=5cos⁡θr = 5\cos\theta enclose a bounded region for 0≤θ≤π0\le \theta \le \pi. Write, but do not evaluate, a sum of definite integrals whose value equals the area of this region. Your expression must clearly indicate the limits of integration and the correct integrand on each sub-interval of θ\theta.

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