Substitution Rule for Indefinite and Definite Integrals.

0:00 Substitution Rule for Indefinite and Definite Integrals.

0:43 Substitution Rule for Indefinite Integrals.

3:57 Substitution Rule for Definite Integrals.

4:24 Example: Integrate ( x + 1 ) ^ 12.

7:43 Example: Integrate 3 times e ^ ( 3x +1).

11:41 Example: Integrate 2x times ( x^2 - 1 )^ 99.

16:51 Example: Integrate (Sin ^ (x)) times (Cos (x)).

Integrals of Even and Odd Functions and the Function Average.

0:00 Integrals of Even and Odd Functions and the Function Average.

0:25 Introduction to Even Functions.

3:56 Introduction to Odd Functions.

6:31 Trig Functions as Odd and Even Functions.

7:58 Neither Odd nor Even?

9:13 Integrals of EVEN Functions RULE.

10:21 Integrals of ODD Functions RULE.

14:05 Example: Integral of Cos (x ) from -pi/2 to pi/2.

16:56 The Average Value of a Function Rule.

22:01 Example: Integral of x^2 from -2 to 2.

23:02 Example: Integral of x^3 from -2 to 2.

23:57 Example: Integral of Cos (x ) from -2Pi to 2Pi.

25:33 Example: Integral of x^9 from -5 to 5.

26:20 Example: Integral of x^2 times Sin (x ) from -Pi to Pi.

27:40 Example: Integral of x^9 -3x^5 + 2x^2 - 10 from -2 to 2.

29:30 Example: Find the Average Value of the Function f(x) = x - x^2 from 0 to 1.