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How would you use a double integral to find the area enclosed by a cardioid?

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Final answer:

To find the area enclosed by a cardioid using a double integral, one needs to set up the integral in polar coordinates and evaluate it.

Step-by-step explanation:

To find the area enclosed by a cardioid using a double integral, we need to set up the integral in polar coordinates. The equation of a cardioid in polar coordinates is given by r = a(1 + cos(theta)), where 'a' represents the distance between the origin and the tip of the cardioid. The integral to find the area enclosed by the cardioid is then given by A = (1/2) ∫[a1, a2] ∫[0, 2π] r dr dθ, where 'r' represents the distance from the origin and 'θ' represents the angle. We can evaluate this integral to find the area of the cardioid.

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