Is [0,∞] e^(-x^3) dx an Improper Integral?

In summary, the conversation is about determining whether the integral [0,infinity] e^(-x^3) dx is improper or not. The first person says yes and believes that it is not improper because its domain is all real. The second person asks for the definition of an improper integral and the third person concludes that it is indeed improper because of the upper limit of integration. The first person then realizes that they are using the definition from Stewart Calculus and agrees that it is improper.
  • #1
Jbreezy
582
0

Homework Statement


It just wants me to tell whether this is improper or not.
[0,infinity] e^(-x^3) dx

Homework Equations




I say Yes

The Attempt at a Solution

 
Physics news on Phys.org
  • #2
I don't see why it would be improper. What's your reasoning?
 
  • #3
I'm not 100 percent sure. I said yes because I think it keeps going it's domain is all real.
 
  • #4
Jbreezy said:

Homework Statement


It just wants me to tell whether this is improper or not.
[0,infinity] e^(-x^3) dx

Homework Equations




I say Yes

The Attempt at a Solution


What definition of "improper integral" are you using?
 
  • #5
Jbreezy said:

Homework Statement


It just wants me to tell whether this is improper or not.
[0,infinity] e^(-x^3) dx

Homework Equations




I say Yes

The Attempt at a Solution

I would call this integral --
$$\int_0^{\infty}e^{-x^3}dx$$
-- improper, because of the upper limit of integration.
 
  • #6
I'm just using the def in stewart calc. I think it is improper thanks.
 

Related to Is [0,∞] e^(-x^3) dx an Improper Integral?

1. What is an Improper Integral?

An Improper Integral is an integral where one or both of the bounds of integration are infinite, or where the integrand function is not defined at certain points within the bounds of integration.

2. How do you determine if an integral is improper?

An integral is considered improper if one or both of the following conditions are met: the bounds of integration are infinite, or the integrand function is not defined at certain points within the bounds of integration.

3. Is [0,∞] e^(-x^3) dx an Improper Integral?

Yes, [0,∞] e^(-x^3) dx is an Improper Integral because the upper bound of integration is infinite.

4. How do you solve an Improper Integral?

To solve an Improper Integral, you must first determine if it is convergent or divergent. If it is convergent, you can use a variety of methods such as the Comparison Test, the Limit Comparison Test, or the Integral Test to evaluate the integral. If it is divergent, the integral cannot be evaluated.

5. What is the significance of [0,∞] e^(-x^3) dx as an Improper Integral?

The significance of [0,∞] e^(-x^3) dx as an Improper Integral lies in its use in various applications in mathematics and physics. It is also a good example of an improper integral that is challenging to solve, making it a common problem in calculus courses.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
979
  • Calculus and Beyond Homework Help
Replies
7
Views
778
  • Calculus and Beyond Homework Help
Replies
13
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
16
Views
3K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Replies
5
Views
732
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
14
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
403
Back
Top