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Skills available for Tennessee high school math standards

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C.F Functions, Graphs, and Limits

C.D Derivatives

C.I Integrals

  • C.I.UI Understanding Integrals

    • C.I.UI.A Demonstrate understanding of a definite integral.

      • C.I.UI.A.1 Define the definite integral as the limit of Riemann sums and as the net accumulation of change.

      • C.I.UI.A.2 Correctly write a Riemann sum that represents the definition of a definite integral.

      • C.I.UI.A.3 Use Riemann sums (left, right, and midpoint evaluation points) and trapezoid sums to approximate definite integrals of functions represented graphically, numerically, and by tables of values.

    • C.I.UI.B Understand and apply the Fundamental Theorem of Calculus.

      • C.I.UI.B.4 Recognize differentiation and antidifferentiation as inverse operations.

      • C.I.UI.B.5 Evaluate definite integrals using the Fundamental Theorem of Calculus.

      • C.I.UI.B.6 Use the Fundamental Theorem of Calculus to represent a particular antiderivative of a function and to understand when the antiderivative so represented is continuous and differentiable.

      • C.I.UI.B.7 Apply basic properties of definite integrals (e.g., additive, constant multiple, translations).

  • C.I.AI Calculate and Apply Integrals

    • C.I.AI.A Apply techniques of antidifferentiation.

      • C.I.AI.A.1 Develop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric).

      • C.I.AI.A.2 Use substitution of variables to calculate antiderivatives (including changing limits for definite integrals).

      • C.I.AI.A.3 Find specific antiderivatives using initial conditions.

    • C.I.AI.B Apply integrals to solve problems.

      • C.I.AI.B.4 Use a definite integral to find the area of a region.

      • C.I.AI.B.5 Use a definite integral to find the volume of a solid formed by rotating a region around a given axis.

      • C.I.AI.B.6 Use integrals to solve a variety of problems (e.g., distance traveled by a particle along a line, exponential growth/decay).