Common Core · AP Calculus AB
FUN-6.C
AP Calculus AB, Unit 6 — Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives (with the constant of integration).
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 6 — Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives.
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
- IntegralsReverse differentiation to find antiderivatives, use definite integrals to measure accumulated area, and pin down the one antiderivative through a given point.Read the lesson →
- Integration by SubstitutionUndo the chain rule: choose u, adjust the constant, integrate powers of an inside function, trigonometric, exponential and logarithm composites and radicals, change the limits of a definite integral, and put x back in terms of u when one is left over.Read the lesson →
What a student should be able to do
- Find the antiderivative of a power of x.
- Evaluate a definite integral with the fundamental theorem of calculus.
- Interpret a definite integral as an area or a total change.
- Remember the constant of integration, and find the particular antiderivative through a given point.
- Choose the substitution u, find du, and work out the constant factor it leaves outside.
- Integrate (ax + b)n, x(x2 + c)n, cos(kx), x ex^2, sqrt(ax + b) and similar composites.
- Recognise the forms that integrate to a logarithm.
- Evaluate a definite integral by changing the limits along with the variable, and rearrange u = x + c into x = u - c when a lone x survives.