September 11, 2014

In this, the fourth section of the course, the topics include:

Interpretations and properties of definite integrals

• Definite integral as a limit of Riemann sums.

• Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.

• Basic properties of definite integrals (examples include additivity and linearity).

Fundamental Theorem of Calculus

• Use of the Fundamental Theorem to evaluate definite integrals.

• Use of the Fundamental Theorem to represent a particular antiderivative and

the analytical and graphical analysis of functions so defined.

Techniques of antidifferentiation

• Antiderivatives following directly from derivatives of basic functions.

• Antiderivatives by substitution of variables (including change of limits for

definite integrals).

Numerical approximations to definite integrals.

• Use of Riemann sums (using left, right, and midpoint evaluation points) and

trapezoidal sums to approximate definite integrals of functions represented

algebraically, graphically, and by tables of values.

- Mathematics > General
- Mathematics > Calculus

- Grade 11
- Grade 12