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Area of circle (double integral and cartesian coordinates)? What would you set the limits if you need to calculate the area of an infinitesimal ring in cartesian coordinates i e ∫ dx ∫ dy ∫ d x ∫ d y where you only want to integrate on the infinitesimal ring I know in polar that will be 2πrdr but how will you get it in caartesian using double integral
Calculus proof for the area of a circle 0 the integral of r (d (theta)) from 0 to 2π is 2πr (the circumference of a circle with radius r), now integrate 2πr (dr) from 0 to r and the answer is πr^2 (the area of a circle of radius r) This is my derivation
Mathematics Stack Exchange Q A for people studying math at any level and professionals in related fields
What is the integral of 1 x? - Mathematics Stack Exchange 16 Answers to the question of the integral of 1 x 1 x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers If we allow more generality, we find an interesting paradox For instance, suppose the limits on the integral are from −A A to +A + A where A A is a real, positive number