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

Question

5928 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-15T23:00:27

# ~~ 5.27037 #

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 #