AP Calculus BC · Unit 6
Integration and Accumulation of Change
In short
Unit 6: Integration and Accumulation of Change in AP Calculus BC covers 13 topics: 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 and 9 more. Open each one for what you need to know, a self-check list and how it is tested on the exam.
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What is in Unit 6: Integration and Accumulation of Change?
Unit 6: Integration and Accumulation of Change
6.1 Exploring Accumulations of Change
- I can evaluate accumulation of change by using geometry in some cases.
6.2 Approximating Areas with Riemann Sums
- I can approximate definite integrals for functions represented graphically, numerically, analytically, and verbally.
- I can approximate definite integrals using left, right, and midpoint Riemann sums, as well as trapezoidal sums, with uniform or nonuniform partitions.
6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
- I can apply the Fundamental Theorem of Calculus to differentiate an accumulation function.
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
- I can represent accumulation functions using definite integrals and interpret their behavior from various representations of the integrand.
6.6 Applying Properties of Definite Integrals
- I can apply properties of definite integrals, including scalar multiplication, sum of functions, reversal of limits, and adjacent intervals.
- I can evaluate definite integrals for functions with removable or jump discontinuities.
6.7 The Fundamental Theorem of Calculus and Definite Integrals
- I can recognize that the function defined by the integral of f(t) from a to x is an antiderivative of f.
- I can apply the Fundamental Theorem of Calculus to evaluate the definite integral of a continuous function over an interval [a, b].
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- I can use indefinite integral notation and remember to include the constant of integration.
- I can apply basic differentiation rules in reverse to find antiderivatives.
- I understand that not all functions have closed-form antiderivatives.
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
- I can determine indefinite integrals and evaluate definite integrals for integrands requiring rearrangements into equivalent forms.
- I can use techniques such as long division and completing the square to rearrange integrands into equivalent forms to find antiderivatives.
6.11 Integrating Using Integration by Parts
- I can determine indefinite integrals and evaluate definite integrals using the integration by parts technique.
6.12 Integrating Using Linear Partial Fractions
- I can determine indefinite and evaluate definite integrals for integrands requiring integration by linear partial fractions.
- I can decompose rational functions into sums of ratios of linear, nonrepeating factors to apply basic integration techniques.
6.13 Evaluating Improper Integrals
- I can identify an improper integral by checking if it has infinite limits or an unbounded integrand.
- I can evaluate improper integrals by setting up and calculating the limits of definite integrals.
Integration and Accumulation of Change: common questions
What is in Unit 6: Integration and Accumulation of Change?
It covers 13 topics: 6.1 Exploring Accumulations of Change; 6.2 Approximating Areas with Riemann Sums; 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation; 6.4 The Fundamental Theorem of Calculus and Accumulation Functions; 6.5 Interpreting the Behavior of Accumulation Functions Involving Area; 6.6 Applying Properties of Definite Integrals; 6.7 The Fundamental Theorem of Calculus and Definite Integrals; 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation; 6.9 Integrating Using Substitution; 6.10 Integrating Functions Using Long Division and Completing the Square; 6.11 Integrating Using Integration by Parts; 6.12 Integrating Using Linear Partial Fractions; 6.13 Evaluating Improper Integrals.
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