How to Integrate - Understand Integration Factors

  • Thread starter yamini
  • Start date
  • Tags
    Integrate
In summary, integration is the process of finding the anti-derivative of a given function, while an integration factor is a mathematical tool used to solve certain types of differential equations. It is recommended to consult tutorials or other resources for more in-depth understanding of these concepts.
  • #1
yamini
22
0
how to integrate?

can anybody let me know how to integrate?

and

about integration factor?
 
Physics news on Phys.org
  • #2
that's an absurdly large question. you either don't know this, or expect people here to write whole chapters out of textbooks for you
 
  • #3
kesh said:
...or expect people here to write whole chapters out of textbooks for you

...which they won't do, so you'll browse through the tutorial section or get some instructing material somewhere on the internet, or, consult a book. :wink:
 
  • #4
radou said:
...which they won't do, so you'll browse through the tutorial section or get some instructing material somewhere on the internet, or, consult a book. :wink:
well i was feeling good humoured enough to check the maths tutorials index before posting my reply. nothing on integration
 
  • #5
Integration and an integration factor are two very different things. One is your basic anti-derivative, and the other is used for exact differentials.

Integration is easy. Just like addition has its inverse law of subtraction, derivatives have its inverse law of integration. So if you want to find an integral you just figure out what function F(x) would give you the function you are given f(x) when you take its derivative. In other words, find a function F(x) such that F'(x)=f(x).

You are a long way off from integration factors.
 

1. What is integration and why is it important?

Integration is the process of combining different elements or parts into a whole. In mathematics, it refers to finding the area under a curve or the accumulation of a quantity over a given interval. It is important because it allows us to solve problems that involve continuous change, such as finding the velocity of an object or the population growth of a species.

2. What are integration factors and how do they work?

Integration factors are constants that are multiplied to one side of an equation to make it easier to integrate. They can be used to simplify complex integrals and make them solvable. Integration factors work by cancelling out the derivative of the factor, leaving only the integral of the original function.

3. How do I determine the appropriate integration factor for a given problem?

The appropriate integration factor for a given problem can be determined by looking at the differential equation and identifying the type of equation it is. For example, if it is a linear equation, the integration factor is the coefficient of the variable. If it is a first-order equation, the integration factor is the inverse of the coefficient of the variable.

4. What are some common integration factors used in calculus?

Some common integration factors used in calculus include e^x, sin(x), cos(x), and 1/x. These factors are often used in solving integrals involving exponential, trigonometric, and inverse trigonometric functions.

5. Are there any tips for effectively integrating using integration factors?

Yes, there are a few tips for effectively integrating using integration factors. First, always check to see if the given equation is in standard form before applying an integration factor. Second, when choosing an integration factor, make sure it cancels out the derivative of the function. Lastly, practice and familiarize yourself with different types of integration factors to become more efficient in solving integrals.

Similar threads

  • Calculus and Beyond Homework Help
Replies
30
Views
398
  • Calculus and Beyond Homework Help
Replies
5
Views
660
  • Calculus and Beyond Homework Help
Replies
9
Views
791
  • Calculus and Beyond Homework Help
Replies
5
Views
741
  • Calculus and Beyond Homework Help
Replies
13
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
642
  • Calculus and Beyond Homework Help
Replies
6
Views
464
  • Calculus and Beyond Homework Help
Replies
3
Views
784
  • Calculus and Beyond Homework Help
Replies
1
Views
806
Back
Top