Math Problem Statement

Find the area lying outside r=4sinθ and inside r=2+2sinθ

Solution

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Math Problem Analysis

Mathematical Concepts

Polar Coordinates
Areas Between Polar Curves
Calculus

Formulas

Area between two polar curves: A = 1/2 ∫(r_outer^2 - r_inner^2) dθ
Trigonometric identity: sin^2θ = (1 - cos(2θ))/2

Theorems

Integral calculus for polar areas

Suitable Grade Level

Undergraduate (Calculus I/II)