K12MATH013: Calculus AB

Upon successful completion of this unit, you will be able to:

• Explain in various ways how the definite integral is equal to a limit of Riemann sums.
• Explain the definite integral of a rate of change over an interval as the change of a quantity over the interval [integral from a to b of f'(x)dx = f(b) - f(a) ].
• Use basic properties of definite integrals (such as additivity and linearity) to solve more complex integrals.
• Find basic antiderivatives based on known derivatives of basic functions.
• Find more complex antiderivatives by substitution of variables and changing of limits.
• Use the FTC to evaluate definite integrals.
• Use the FTC to represent a particular antiderivative both analytically and graphically.
• Use appropriate integrals to model physical, biological, and economic scenarios.
• Use appropriate definite integrals in other situations by setting up an approximating Riemann sum and taking its limit in: Finding the area of a region.
• Finding the volume of a solid with known cross sections.
• Finding the average value of a function.
• Finding the distance travelled by a particle along a path.
• Finding an accumulation function or value given a rate of change function.
• Find specific antiderivatives given initial conditions (especially involving motion along a line).
• Solve separable differential equations and use them in modeling (specifically studying y'= ky and exponential growth).
• Use Riemann sums (left, right, and midpoint) to approximate definite integrals of functions represented algebraically, graphically, and by tables of values.
• Use trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values.