Common Core · AP Calculus AB
CHA-4.C
AP Calculus AB, Unit 8 — Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 2 skills that cover it
- Applications of IntegralsPut the definite integral to work: the area between two curves, the average value of a function, the derivative of an accumulation function, displacement against distance, substitution for a composite integrand, and total change from a rate in context.Read the lesson →
- Motion Along a LineRead a moving particle from its position, velocity or acceleration: when it stops and turns, when it speeds up or slows down, how far it travels against how far it ends up, and where it is from where it started.Read the lesson →
What a student should be able to do
- Find the area between two curves, and the area against the axis where a curve dips below.
- Find the average value of a function on an interval.
- Differentiate an accumulation function with the first part of the fundamental theorem.
- Find displacement, distance and net change with an integral, using substitution where the integrand asks for it.
- Find when a particle is at rest and when it changes direction, from a formula or a velocity graph.
- Decide whether a particle is speeding up or slowing down from the signs of velocity and acceleration.
- Find total distance and displacement over an interval, splitting the journey at every turn.
- Recover position from velocity, and velocity from acceleration, with an initial condition, including an object thrown straight up.