Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.2 Length of a Plane Curve, #30 · Calculus · Applications of integrals

The area of an ellipse is

The area of an ellipse is $π ab$ . The area of a strip around it (width $Δ$ ) is $π (a + Δ) (b + Δ) - π ab \approx π (a + b) Δ$ . The distance around the ellipse seems to be $π (a + b)$ . But this distance is impossible to find—what is wrong?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.2 Length of a Plane Curve, #30

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