Chapter Contents

• Methods of Integration
• 1. Integration: The General Power Formula
• 2. Integration: The Basic Logarithmic Form
• 3. Integration: The Exponential Form
• 4. Integration: The Basic Trigonometric Forms
• 5. Integration: Other Trigonometric Forms
• 6. Integration: Inverse Trigonometric Forms
• 7. Integration by Parts
• 8. Integration by Trigonometric Substitution
• 9. Integration by Use of Tables
• Table of Common Integrals
• 10. Integration by Reduction Formulae
• 11. Integration by Partial Fractions
• Methods of Integration Problem Solver

• Comments, Questions?

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From the math blog...

1. Integration: The General Power Formula

by M. Bourne

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

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

Example 1: Integrate:

Answer

Example 2: Integrate:

Answer

Example 3: Integrate:

Answer

Example 4: Integrate:

Answer

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

Answer

Exercises

Integrate each of the following functions:

1.

Answer

2.

Answer

3.

Answer

4.

Answer

5. Find the equation of the curve for which 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:

Answer