# Integration and accumulation of change

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.

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Length | 13 segments |

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Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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Rating | Not enough ratings |
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Length | 13 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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