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: eu.
Example 1: 
Example 2: 
Example 3: 
Here is the LiveMath solution to this problem.
Example 4:
In the theory of lasers, we see
where a, I0 and T are constants. Find E.
Exercises
Integrate each of the given functions.
1. 
2. 
3. 
4. Find the equation of the curve
for which 
if the curve passes through
(1,0).
Application - Volume of Solid of Revolution
The area bounded by the curve y = ex, 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.)
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