How do you calculate the arc length of the curve y=x^2 from x=0 to x=4?
1 Answer
May 16, 2018
Use the arc length formula.
Explanation:
y=x^2
y'=2x
Arc length is given by:
L=int_0^4sqrt(1+4x^2)dx
Apply the substitution
L=1/2intsec^3thetad theta
This is a known integral:
L=1/4[secthetatantheta+ln|sectheta+tantheta|]
Reverse the substitution:
L=1/4[2xsqrt(1+4x^2)+ln|2x+sqrt(1+4x^2)|]_0^4
Hence
L=2sqrt65+1/4ln(8+sqrt65)