Arc Length of a Spiral-Like Parametric Curve
Calculus
Find the exact arc length of the curve parametrized by
\[
x(t)=t\sin t,\qquad y(t)=t\cos t
\]
as the parameter \(t\) varies over the closed interval \(0\le t\le 1\).
A$\frac{\sqrt2}{2}+\frac12\ln(1+\sqrt2)$
B$\sqrt2+\ln(1+\sqrt2)$
C$\frac{\sqrt2}{2}+\ln(1+\sqrt2)$
D$\frac12\ln(2+\sqrt2)$