← MATH 01131 · Calculus II
MATH 01131 · Parametric & polar (often)
Polar area / graphing r(θ)
Definition
Polar: x=r cosθ, y=r sinθ. Area of a polar region: (1/2)∫ₐᵇ [r(θ)]² dθ. Graph by plotting key θ and knowing rose/cardioid/limaçon families.
Read this
r<0 means going opposite the ray θ (depending on convention taught).
Find intersections carefully — same point can have multiple (r,θ) pairs.
Convert to Cartesian when recognition helps (r²=x²+y²).
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
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Try this
Attempt each problem first, then open the worked solution.
1.Area of one petal of r=sin(2θ).