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:

math expression

It is remarkable because the integral is the same as the expression we started with: eu.

Example 1: math expression

Example 2: math expression

Example 3: math expression

Example 4:

In the theory of lasers, we see

math expression

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

Exercises

Integrate each of the given functions.

1. math expression

2. math expression

3. math expression

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

Didn't find what you are looking for on this page? Try search:

Find your integral using Wolfram|Alpha!

This next search box allows you to enter your math problem and Mathematica solves it for you. (It's free!)

See how to enter math.

Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Calculus Lessons on DVD

get MathTutorDVDs

Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

Ready for a break?

shadow factory

Play a math game.

(Well, not really a math game, but each game was made using math...)

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Share IntMath!

This page has

  • 22 Facebook likes & comments

Short URL for this Page

Save typing! You can use this URL to reach this page:

intmath.com/intexpon

axs