`x=arcsint , y=ln(sqrt(1-t^2)) , 0

Arc length of a curve C described by the parametric equations x=f(t) and y=g(t), where f' and g' are continuous on [a,b] and C is traversed exactly once as t increases from a to b, then the length of the curve is given by,

We are given:

Now let's evaluate arc length by using the stated formula,

Using partial fractions...

Arc length of a curve C described by the parametric equations x=f(t) and y=g(t), where f' and g' are continuous on [a,b] and C is traversed exactly once as t increases from a to b, then the length of the curve is given by,

We are given:

Now let's evaluate arc length by using the stated formula,

Using partial fractions integrand can be written as :

Take the constant out and use the standard integral:

Arc length of the curve on the given interval is