AP Calc Review for Meself

v(t)

s’(t)

a(t)

s’’(t) or v’(t)

particle moves right

v(t) > 0

particle moves left

v(t) < 0

particle speeds up

v(t) and a(t) are the same sign

particle slows down

v(t) and a(t) have opposite signs

total distance

|v(t)|

displacement

integral [a,b] v(t) dt

displacement and total distance

are not the same

position at time t

s(t) = s(t0) + int [t0, t] v(u) du

particle changes direction

when v(t) = 0 AND when v(t) changes signs

net change in quantity from t=a to t=b

integral [a,b] R(t) dt

amount at time b

amount at time a + integral [a,b] R(t) dt

quantity increasing

r(t) > 0

quantity decreasing

r(t) < 0

average rate of change

[f(b) - f(a)] / (b - a)

average value of f on [a,b]

(1/(b-a)) integral [a,b] f(x) dx

net change theorum

integral [a,b] f’(x) dx = f(b) - f(a)

net change for in / out problems

integral (in rate) - integral(out rate)

units what?

MATTER!!!!

average value and average rate of change

ARE NOT THE SAME