The

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

### Mission Foundations

- Power rule (advanced)
- Special derivatives
- Product rule
- Chain rule on three functions
- Applications of differentiation in biology, economics, physics, etc.
- Related rates
- Partial fraction expansion
- Modeling with periodic functions 2

### Integrals

- Finding antiderivatives
- Graphs of antiderivatives
- Finding the constant of integration
- Area under a rate function equals net change
- Using rectangles to approximate area under a curve
- Riemann sums and sigma notation
- Trapezoid rule
- The definite integral as the limit of a Riemann sum
- Evaluating a definite integral from a graph
- Properties of integrals
- Functions defined by integrals
- The fundamental theorem of calculus
- Area between a curve and an axis
- Evaluating definite integrals
- Improper integrals

### Integration techniques

- Integration by parts
- Integration by u-substitution
- Integration by the reverse chain rule
- Integration using trigonometric identities
- Integration using trigonometric substitution
- Integration of rational functions by division and partial fractions

### Integration applications

- Area between two curves
- Average value of a function
- Arc length of functions in one variable
- Volumes of solids of known cross-section
- Volumes of solids of revolution, discs, and washers
- Volumes of solids of revolution by shells
- Area enclosed by polar graphs
- Arc length of polar curves

### Sequences, series, and function approximation

- Understanding sequences
- Find the next term of a geometric sequence, given the first few terms
- Find any term of a geometric sequence, given the formula of the sequence
- Convergence and divergence of sequences
- Arithmetic series
- Understanding series
- Convergence and divergence of series
- Calculating finite geometric series
- Infinite geometric series
- nth term test
- Ratio test
- Direct and limit comparison tests
- Alternating series
- Alternating series remainder
- Creating power series from geometric series using algebra
- Creating power series from geometric series using differentiation and integration
- Maclaurin series for sin x, cos x, and e^x
- Integration and differentiation of power series
- Finding taylor series

### AP Calculus practice questions

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