Area of a "curved rectangle" (bonus: why dxdy=rdrdθ)

We will investigate the area of a circular curved rectangle. We have discussed this shape in the surface area of revolution:    • Integral formulas for area, volume (d...  . We can also use this area of a curved rectangle to see why dxdy=rdrdθ when we do double integrals.Here's how we can use change of coordinate to evaluate the Gaussian integral of e^(-x^2) from 0 to inf:    • How Gauss solved the integral of e^(-...  
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