Question

Which of the following definite integrals represents the arc length of the curve
y=sqrt(1+x^2)
between x = -1 and x = +1 ?

Answer 1

\[\int\limits_{-1}^{1}\frac{ \sqrt{1+2x^2} }{ \sqrt{1+x^2} }dx\]

Answer 2

\[\int\limits_{-1}^{1}\frac{ \sqrt{4+5x^2} }{ \sqrt{4+4x^2} }dx\]