What is the arc length of $f(x)=sqrt(4-x^2)$ on $x in [-2,2]$ ?

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Answer 1 · 2015-11-08T02:51:33

arc length $=intsqrt [1+(dy/dx)^2]dx$

$dy/dx = (-x)/[sqrt(4-x^2)]$

$(dy/dx)^2=x^2/(4-x^2)$

arc length $=int sqrt[1+x^2/(4-x^2)]dx=2int1/sqrt(4-x^2)dx$

$=arcsin(x/2)+C$

Finally, evaluate over [-2,2]

arc length $=2pi$

hope that helped

What is the arc length of f(x)=sqrt(4-x^2) f(x)=sqrt(4-x^2) on x in [-2,2]x in [-2,2]?