It's a calc question please help!

Question

A particle moves along the x-axis so that at any time t, 0_<t_<5, the velocity is given by v(t)=sint + e^-t. At t=0 the particle is at the origin (x(0)=0).
A) Find all values of t, such that the velocity is zero
B) Find an equation, x(t)

Answer 1

A.  solve sin t = -e^-t on a graphing calculator (empirical result).

 

B.  x(t) = ∫ (sin t + e^-t)dt = -cos t - e^-t + c.

 

x(0) leads to c = 2.