Intergral Calculus question!!!!!!?

Question

Use the given velocity function and initial position to estimate the final position s(b). Round your final answer to the nearest integer.
v(t) = 31(1 − e−5t), s(0) = 0, b = 6
s(b) = ?

Answer 1

s = integral(v(t) dt))

= integral(31(1-e^-5t))dt

What you really have is a differential equation. Anyway

s = 31*(t +1/5e^-5t) + c and you need ot satisfy

s(0) = 0 = 31/5 + c ---> c = -31/5


Then s(t=6) = 31*[(6+1/5e^-30)-1/5] e^-30 is really small so set it equal to zero

s(t=6) = 31*35/6

Answer 2

1116et ??? i dont i think if i sovled it right thats the right answer.