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