How do you find the arc length of the curve y=2sinx over the interval [0,2pi]?

1 Answer
Jan 15, 2017

~~ 5.27037

Explanation:

The Arc Length of curve y=f(x) is calculated using the formula:

L = int_a^b sqrt(1+(dy/dx)^2) \ dx

So with f(x) = 2sinx, we get:

dy/dx = 2cosx

And so the required Arc Length is given by:

L = int_0^pi sqrt(1+(2cosx)^2) \ dx
\ \ = int_0^pi sqrt(1+4cos^2x) \ dx

This integrand does not have an elementary solution

Using Wolfram Alpha this integral evaluates to:

L ~~ 5.27037