Could someone verify I am understanding this Calculus problem correctly, please?

Question

Hi, I am working on a problem and I think I have it solved, but would just like to make sure that I have done it correctly, if possible. I appreciate anyone taking the time to help me.

Problem:

"The velocity of a falling object may be modeled by v(t) = 20(1-e^-0.5t) meters per second for the first ten seconds. Calculate the distance the object has fallen in the first ten seconds of the fall."

My Solution:

∫ 20(1-e^-0.5t)dt = 20∫1dt - 20∫e^-t/2dt

solving for first integral: ∫1dt = t

solving for second integral (u = - t/2, -1/2 = du/dt, -2du = dt): ∫e^-t/2dt => -2∫e^udu = -2e^u = -2e^-t/2

putting it all together: 20∫1dt - 20∫e^-t/2dt = 40e^-t/2+20t + C

Then evaluate the definite integral: 40e^-10/2 + 20(10) - [ 40e^-0/2 + 20(0)] ≈ 160.3 meters

Again, thank you for the help, ahead of time.

Answer 1

20∫_{(from t=0 to t=10)}[1−e^-0.5t]dt equals 20[t + 2e^-0.5t|_{(from t=0 to t=10)}]

which gives 20[10 + 2e^-5−0−2] or 160.2695179 Meters.