K–12 teaching and learning · from the UNC School of Education
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- My LEARN NC
- Objective 3.01
- Explore and interpret the concept of the definite integral.
- Compute Riemann sums using left, right, and midpoint evaluation points.
- Find the definite integral as a limit of Riemann sums over equal subdivisions.
- Find the definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.
- Identify basic properties of definite integrals.
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- Objective 3.02
- Apply standard techniques of anti-differentiation.
- Find anti-derivatives following directly from derivatives of basic functions.
- Find anti-derivatives by substitution of variables. (including change of limits for definite integrals).
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- Objective 3.03
- Apply and interpret the Fundamental Theorem of Calculus.
- Use the Fundamental Theorem to evaluate definite integrals.
- Use the Fundamental Theorem to represent a particular anti-derivative, and the analytical and graphical analysis of functions so defined.
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- Objective 3.04
- Define and use appropriate integrals in a variety of applications.
- Interpret the integral of a rate of change to give accumulated change.
- Find specific anti-derivatives using initial conditions.
- Set up and use an approximating Riemann sum or trapezoidal sum and represent its limit as a definite integral.
- Find the area of a region.
- Find the volume of a solid with known cross sections.
- Find the average value of a function.
- Find the distance traveled by a particle along a line.
- Solve separable differential equations and use them in modeling. In particular, study the equation y' = ky and exponential growth.
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