Georgia standard · Mathematics

`C.GSR.5`Fundamental Theorem of Calculus

Analyze the relationship between the derivative and the integral using the Fundamental Theorem of Calculus.

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Expectations

Evaluate and interpret definite integrals.
- C.GSR.5.1
  Use Riemann sums to approximate values of definite integrals.
- C.GSR.5.2
  Interpret a definite integral as a limit of Riemann sums.
- C.GSR.5.3
  Find the exact value of a definite integral using geometric formulas on a coordinate plane.
- C.GSR.5.4
  Demonstrate the use of properties of definite integrals.
- C.GSR.5.5
  Apply the Fundamental Theorem of Calculus as an interpretation of the accumulation in the rate of change of a function as equivalent to the change in the antiderivative over the interval.
Find the antiderivative of indefinite integrals.
- C.GSR.5.6
  Apply Fundamental Theorem of Calculus to indefinite integrals to represent the family of antiderivatives.
- C.GSR.5.7
  Apply integration by substitution to definite and indefinite integrals.

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