Length of a curve

The length of a curve from point a to point b can be found using an integral of the first derivative of the equation:

equation = f(x)

first derivative = f '(x)

length = ∫sqr(1+f '(x)²)dx

For the previous example of heating a liquid, the first derivative of the equation was f '(t)=30e^−0.3t

so the length of the curve from 0 to 5 minutes would be:

∫sqr(1+30e^−0.3t2)dt