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1. Integration: The General Power Formula

by M. Bourne

In this section, we apply this formula to trigonometric, logarithmic and exponential functions:

(We met this substitution formula in an earlier chapter: General Power Formula for Integration.)

Example 1: Integrate: math expression

Answer

Example 2: Integrate:

Answer

Example 3: Integrate:

Answer

Example 4: Integrate: math expression

Answer

Example 5: Find the equation of the curve for which math expression if the curve passes through (1,2).

Answer

Exercises

Integrate each of the following functions:

1. math expression

Answer

2. math expression

Answer

3. math expression

Answer

4. math expression

First, the LiveMath solution to this problem.

LIVEMath

Answer

5. Find the equation of the curve for which math expression if the curve passes through (2,1).

Answer

6. A space vehicle is launched vertically from the ground such that its velocity v (in km/s) is given by

where t is the time in seconds. Find the altitude of the vehicle after 10.0 s.

The graph of is as follows:

math expression

Answer

Methods of Integration

2. Integration: The Basic Logarithmic Form

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