Calculating the length of a curve.
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Find the length of the curve y=e^-x, 0<_x<_1
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By definition length of curve:
l = integration(0,1) [sqrt{ 1 + (dy/dx)^2}] dx
here dy/dx = - e^(-x)
=> l= integ(0,1)[ sqrt{1 + {-e^(-x)}^2}] dx
=> l = int(0,1) [sqrt{1 + e^(-2x)}] ...
Solution Summary
The length of a curve is calculated.
$2.49