A Definite integral where solution. involves infinity - infinity

In summary, the conversation discusses how to evaluate an integral, specifically looking at one with limits of integration and using partial fractions to solve it. The poster is advised to start by considering the integral with specific limits and then taking the limit as the upper bound approaches infinity. The conversation also mentions a previous post with images.
Physics news on Phys.org
  • #2
What work have you done on this? What makes you think that it is of the indeterminate form in the thread title?

When you start in on this, if you haven't done so already, look at the integral with limits of integration 0 and b, do the integration, and then take the limit as b approaches infinity.

In doing the integral, I would go at this using partial fractions.
 
  • #4
See my reply in the other thread.
 

1. What is a definite integral?

A definite integral is a mathematical concept used in calculus to find the area under a curve between two points on the x-axis. It represents the sum of infinitely many infinitely small rectangles that make up the area.

2. What does it mean when the solution to a definite integral involves infinity - infinity?

This means that the integral is divergent, or does not have a finite solution. It could also indicate that the function being integrated is undefined or approaches infinity at one or both of the limits of integration.

3. How do you solve a definite integral with infinity - infinity?

If the function being integrated is undefined or approaches infinity at one or both of the limits of integration, the integral is divergent and does not have a finite solution. However, if the function is well-behaved and the limits of integration are both infinity, the solution can be found using techniques such as integration by parts or substitution.

4. Can a definite integral with infinity - infinity have a finite solution?

No, a definite integral with infinity - infinity is divergent and does not have a finite solution. This means that the integral cannot be evaluated to a specific, finite number.

5. What are some real-world applications of definite integrals with infinity - infinity?

Definite integrals with infinity - infinity are often used in physics and engineering to model and solve problems involving infinite quantities. For example, the work done by a force that varies with distance, or the total mass of an object with varying density, can be represented by definite integrals with infinite limits.

Similar threads

  • Calculus and Beyond Homework Help
Replies
14
Views
2K
  • Calculus and Beyond Homework Help
Replies
8
Views
7K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
929
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
3K
  • Calculus and Beyond Homework Help
Replies
2
Views
960
  • Calculus and Beyond Homework Help
Replies
4
Views
764
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
Back
Top