Understanding the Integral of e^x: Solving for \int_0^1 e^{-3x} dx Explained

  • Thread starter digink
  • Start date
  • Tags
    Integral
In summary, the conversation discusses the use of a constant (-1/3) when solving for the integral of e^-3x, and how it is used to get rid of the -3 in the derivative. This constant is necessary because in the integral, there is no -3 present. The conversation also touches on the importance of remembering to use the derivative of e^x when it is raised to a power, such as 3x.
  • #1
digink
26
0
Ok I know that the [tex]\int e^x = e^x + C[/tex]

now I don't understand this problem.

[tex]\int_0^1 e^{-3x} dx = -(1/3)e^{-3(0)} - -(1/3)e^{-3(1)}[/tex]
[tex]= 1/3(1- e^{-3} )[/tex]

Where does the 1/3 come from?
 
Physics news on Phys.org
  • #2
anyone?? have to study for a test any help would be greatly appreciated.

I just want to know where the constant -1/3 came from.
 
  • #3
Because...

*I'm using -> to point to the derivative.

e^x -> e^x

e^3x -> 3e^3x

e^-3x -> -3e^-3x

See how the 3 came up? The -1/3 is used to get rid of the -3 because in the integral we don't have a -3.

-1/3e^-3x -> e^-3x

Note: I know it's sloppy, but you should get the idea.
 
  • #4
JasonRox said:
Because...

*I'm using -> to point to the derivative.

e^x -> e^x

e^3x -> 3e^3x

e^-3x -> -3e^-3x

See how the 3 came up? The -1/3 is used to get rid of the -3 because in the integral we don't have a -3.

-1/3e^-3x -> e^-3x

Note: I know it's sloppy, but you should get the idea.


wow I feel really stupid to forget that lol, I forgot that when [tex]e^x[/tex] is raised to something like 3x you use the derivative of that times the original [tex]e^x[/tex] function.

thanks :D
 
  • #5
I forget it sometimes to because your so used to copying e^x down as the derivative.

Good Luck!
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to find the total value of a function between two points on the graph.

2. Why do we need to use integrals?

Integrals are useful in many fields of science, including physics, engineering, and economics. They allow us to find the total value of a function, which can help us make predictions and solve real-world problems.

3. How do I solve an integral?

Solving an integral involves finding the antiderivative of a function and evaluating it between the given limits. This can be done using various techniques, such as substitution, integration by parts, or trigonometric identities.

4. What is the difference between a definite and indefinite integral?

A definite integral has specific limits of integration, meaning that it gives a numerical value. An indefinite integral does not have limits and represents a family of functions, which can be used to find the value of a function at any point.

5. Can I use a calculator to solve integrals?

Yes, there are many online tools and calculators available that can help you solve integrals. However, it is important to understand the concept and techniques behind integration in order to use them effectively.

Similar threads

Replies
3
Views
1K
Replies
3
Views
219
Replies
2
Views
833
Replies
19
Views
2K
Replies
2
Views
917
Replies
4
Views
644
Replies
1
Views
833
Replies
3
Views
1K
  • Calculus
Replies
6
Views
1K
Back
Top