# Calculating the length of a curve.

Find the length of the curve y=e^-x, 0<_x<_1

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#### Solution Preview

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.

$2.19