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...

6. Integration: Inverse Trigonometric Forms

by M. Bourne

Using our knowledge of the derivatives of inverse trigonometric identities that we learned earlier and by reversing those differentiation processes, we can obtain the following integrals:

Example 1: Integrate: .

Answer

Example 2: Integrate:

Answer

Example 3: Find the area bounded by the curve and the lines x = 0, y = 0 and x = 2.

Answer

Caution:

There are a number of integrals of forms which look very similar to the above but are actually different, e.g.

We will develop methods to solve these in a later section. (See Integration by Trigonometric Substitution.)

Exercises

Integrate each of the given functions:

1.

Answer

2.

Answer

3.

Answer

4. Find the area bounded by the curve and the lines x = 0, y = 0 and x = 1.

Answer

This is not the answer ... it is a corruption of a .gif file containing the answer!!:

[This happened in MS Word during a period of great instability - the computer's and mine...^_^]