A particle moves along the x-axis that at any time t, 0<=t<=5, its velocity is given by v(t)=sin(t)+e^-t. Went t=0, the particle is at the origin.
(a) Write an expression for the position function, x(t), of the particle at any time t, 0<=t<=5.
(b) What are all values of t for which the particle is at rest?
(c) For 0<=t<=5, find the average value of the position function determined in part (a).
(d) Find the total distance traveled by the particle from t=0 to t=5.