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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:

Here is the LiveMath solution to this problem.

LIVEMath

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.

Answer

2. math expression

Answer

3. math expression

Answer

4. Find the equation of the curve for which math expression 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

2. Integration: The Basic Logarithmic Form

4. Integration: The Basic Trigonometric Forms

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