Answer
$\approx{3.820}$
Work Step by Step
The formula for the arc length is
$s=\int_{a}^b \sqrt{1 + (y')^2} dy$
Differentiate $y = \sin{x}$ with respect to x.
$y' =\cos{x}$
Substitute the value of y' in $1 + (y')^2$
$1+(y')^2=1+{\cos{^2}{x}}$
Substitute the value of $1 + (y')^2$ in the formula for the arc length $s=\int_{a}^b \sqrt{1 + (y')^2} dy$
Solve for the distance s
$s=\int_{0}^{\pi}\sqrt{1+\cos{^2}{x}} dx$
$\approx{3.820}$
