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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3. Integration: The Exponential Form

by M. Bourne

By reversing the process in obtaining the derivative of the exponential function, we obtain the remarkable result:

It is remarkable because the integral is the same as the expression we started with: e^u.

Example 1:

Answer

Example 2:

Answer

Example 3:

Answer

Example 4:

In the theory of lasers, we see

where a, I₀ and T are constants. Find E.

Answer

Exercises

Integrate each of the given functions.

1.

Answer

2.

Answer

3.

Answer

4. Find the equation of the curve for which if the curve passes through (1,0).

Answer

Application - Volume of Solid of Revolution

The area bounded by the curve y = e^x, the x-axis and the limits of x = 0 and x = 3 is rotated about the x-axis. Find the volume of the solid formed. (You may wish to remind yourself of the volume of solid of revolution formula.)

Answer