Polar Area Example

AP Calculus · Axiom Academy

Finding the area of a cardioid Step 1: Identify the limits of integration The cardioid is a complete closed curve as θ goes from 0 to 2π. Integration limits: θ from 0 to 2π Step 2: Apply the polar area formula We need to expand before integrating Step 6: Evaluate the antiderivative ✓ Final Answer: The total area enclosed by the cardioid is Verification: Notice how the trig identity made the integral solvable. Without it, we'd have a very difficult integral!

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