Chapter 5, Problem 45RE

Displacement from velocity A particle moves along a line with a velocity given by v(t) = 5 sin πt starting with an initial position s(0) = 0. Find the displacement of the particle between t = 0 and t = 2, which is given by $s(t)={\displaystyle {\int }_0^{2}v(t)dt}$. Find the distance traveled by the particle during this interval, which is ${\displaystyle {\int }_0^2|v(t)|dt}$.