Math Problem Statement
Find the area of the inside loop of the limacon r=4+8sin(theta)
Solution
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Math Problem Analysis
Mathematical Concepts
Polar Coordinates
Integral Calculus
Limaçon Curves
Area Calculation in Polar Coordinates
Formulas
Area of a polar region: A = (1/2) ∫ r^2 dθ
Limaçon equation: r = a + b*sin(θ) or r = a + b*cos(θ)
Trigonometric identity: sin^2(θ) = (1 - cos(2θ)) / 2
Theorems
Integral calculus for polar areas
Symmetry considerations in polar curves
Suitable Grade Level
College Level (Calculus II or above)
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