Integration and accumulation of change

This course is a part of AP®︎ Calculus AB, a 10-course Topic series from Khan Academy.

The definite integral of a function gives us the area under the curve of that function. Another common interpretation is that the integral of a rate function describes the accumulation of the quantity whose rate is given. We can approximate integrals using Riemann sums, and we define definite integrals using limits of Riemann sums. The fundamental theorem of calculus ties integrals and derivatives together and can be used to evaluate various definite integrals.

This course contains 13 segments:

Exploring accumulations of change

Approximating areas with Riemann sums

Riemann sums, summation notation, and definite integral notation

The fundamental theorem of calculus and accumulation functions

Interpreting the behavior of accumulation functions involving area

Applying properties of definite integrals

The fundamental theorem of calculus and definite integrals

Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule

Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals

Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals

Integrating using substitution

Integrating functions using long division and completing the square

Optional videos

Some things are not explicitly required by the AP Calculus AB course, but many teachers cover them and we also find them useful. We've gathered those optional videos here for your convenience.