Examples for

Arc Length

Arc length is the measure of the length along a curve. For any parameterization, there is an integral formula to compute the length of the curve. There are known formulas for the arc lengths of line segments, circles, squares, ellipses, etc.

Arc Length

Compute lengths of arcs and curves in various coordinate systems and arbitrarily many dimensions.

Compute the arc length of common curves:

arc length of circle
cardioid length

Compute the arc length of a curve:

arc length of y=x^2 from x=0 to 1
length of e^-x^2 for x=-1 to x=1

Specify a curve in polar coordinates:

arc length of polar curve r=t*sin(t) from t=2 to t=6

Specify the curve parametrically:

arclength x(t)=cos^3 t, y(t)=sin^3 t for t=0 to 2pi
length of the curve {x=2cos(t), y=2sin(t), z=t} from 0 to 7

Compute arc length in arbitrarily many dimensions:

arc-length (t,t,t,t^3,t^2) from 1 to Pi

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Step-by-Step Solutions for Applications of Calculus

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