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a) Show that the area of a closed curve in the xy-plane can be expressed A == f(ndy – ydz) = f(zỷ – yà)dt ±)dt where the integral is taken counterclockwise around the curve and x(t) and y(t) ar parametric representations of a curve. b) What shape should a closed curve of given constant length be in order to enclose th greatest possible area?

a) Show that the area of a closed curve in the xy-plane can be expressed A == f(ndy – ydz) = f(zỷ – yà)dt ±)dt where the integral is taken counterclockwise around the curve and x(t) and y(t) ar parametric representations of a curve. b) What shape should a closed curve of given constant length be in order to enclose th greatest possible area?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Show that the area of a closed curve in the ry-plane can be expressed (xdy – ydæ) = 5 $ (xỷ – yä)dt where the integral is taken counterclockwise around the curve and r(t) and y(t) are parametric representations of a curve. b) What shape should a closed curve of given constant length be in order to enclose the greatest possible area?
Transcribed Image Text:a) Show that the area of a closed curve in the ry-plane can be expressed (xdy – ydæ) = 5 $ (xỷ – yä)dt where the integral is taken counterclockwise around the curve and r(t) and y(t) are parametric representations of a curve. b) What shape should a closed curve of given constant length be in order to enclose the greatest possible area?
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