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