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

The Integral calculus dashboard.

Mission Specifics

Mission Foundations

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

Integration techniques

  1. Integration by parts
  2. Integration by u-substitution
  3. Integration by the reverse chain rule
  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. Find the next term of a geometric sequence, given the first few terms
  3. Find any term of a geometric sequence, given the formula of the sequence
  4. Convergence and divergence of sequences
  5. Arithmetic series
  6. Understanding series
  7. Convergence and divergence of series
  8. Calculating finite geometric series
  9. Infinite geometric series
  10. nth term test
  11. Ratio test
  12. Direct and limit comparison tests
  13. Alternating series
  14. Alternating series remainder
  15. Creating power series from geometric series using algebra
  16. Creating power series from geometric series using differentiation and integration
  17. Maclaurin series for sin x, cos x, and e^x
  18. Integration and differentiation of power series
  19. Finding taylor series

AP Calculus practice questions

Users can view other Math Missions here.

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