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Basics of Integrals

Having basic tools and techniques is essential for success.

5A

Understanding the Concept of an Integral

  • Explain the "net change" an integral finds
  • Explain what an integral calculates
  • Find integral values for functions whose graphs are piece-wise, simple geometry forms
  • Recall and apply properties of integrals
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5B

Estimating Integrals

  • Use various types of Riemann sums to estimate integral values
  • Use other methods to approximate integral values
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5C

Understanding the Mean Value Theorem for Integrals

  • Explain the meaning of the MVT
  • Find values guaranteed by the MVT
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5D

Fundamental Theorem of Calculus Part 1: The Area Accumulator

  • Find values for area accumulator functions
  • Graph area accumulator functions
  • Find derivatives of area accumulator functions
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5E

Fundamental Theorem of Calculus Part 2: The Evaluative Form

  • Find basic antiderivatives
  • Evaluate definite integrals with basic antiderivatives
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5F*

Understanding Improper Integrals

  • Evaluate improper integrals with an infinite bound
  • Evaluate improper integrals with an infinite discontinuity
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