Integral calculus Math Mission

The Integral calculus Math Mission is a set of skills on Khan Academy. This mission consists of Integral calculus skills.

Mission Foundations

 * 1) Power rule
 * 2) Special derivatives
 * 3) Product rule
 * 4) Chain rule on three functions
 * 5) Applications of differentiation in biology, economics, physics, etc.
 * 6) Related rates
 * 7) Partial fraction expansion
 * 8) Modeling with periodic functions 2

Integrals

 * 1) Antiderivatives
 * 2) Indefinite integrals
 * 3) Area under a rate function equals net change
 * 4) Using rectangles to approximate area under a curve
 * 5) Riemann sums and sigma notation
 * 6) Trapezoid rule
 * 7) The definite integral as the limit of a Riemann sum
 * 8) Evaluating a definite integral from a graph
 * 9) Properties of integrals
 * 10) Area between a curve and an axis
 * 11) Functions defined by integrals
 * 12) The fundamental theorem of calculus
 * 13) Evaluating definite integrals
 * 14) Improper integrals

Integration techniques

 * 1) Integration by parts
 * 2) Integration by the reverse chain rule
 * 3) Integration by u-substitution
 * 4) Integration using trigonometric identities
 * 5) Integration using trigonometric substitution
 * 6) Integration of rational functions by division and partial fractions

Integration applications

 * 1) Area between two curves
 * 2) Average value of a function
 * 3) Arc length of functions in one variable
 * 4) Volumes of solids of known cross-section
 * 5) Volumes of solids of revolution, discs and washers
 * 6) Volumes of solids of revolution by shells
 * 7) Area enclosed by polar graphs
 * 8) Arc length of polar curves

Sequences, series, and function approximation

 * 1) Understanding sequences
 * 2) Geometric sequences 1
 * 3) Geometric sequences 2
 * 4) Convergence and divergence of sequences
 * 5) Arithmetic series
 * 6) Understanding series
 * 7) Convergence and divergence of series
 * 8) Calculating finite geometric series
 * 9) Geometric series of constants
 * 10) Ratio test
 * 11) Direct and limit comparison tests
 * 12) Alternating series
 * 13) Alternating series remainder
 * 14) Creating power series from geometric series using algebra
 * 15) Creating power series from geometric series using differentiation and integration
 * 16) Maclaurin series for sin x, cos x, and e^x
 * 17) Integration and differentiation of power series
 * 18) Finding taylor series
 * 19) nth term test

AP Calculus practice questions
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