Learning Partial Integration: Step-by-Step Guide

In summary, the conversation is about someone asking for help with partial integration and clarification on whether it means integration by parts or integration of a multivariable function. TheDestroyer then clarifies that they need help with integration and differentiation in general, and the conversation continues with a specific integration problem being discussed.
  • #1
TheDestroyer
402
1
Hi Guyz, Any one here can teach me the Partial Integration Step-by-Step?

I need to know every atom in the section, i tried to understand the previous written threads but didn't,

Thanks ...
 
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  • #2
Originally posted by TheDestroyer
Hi Guyz, Any one here can teach me the Partial Integration Step-by-Step?

I need to know every atom in the section, i tried to understand the previous written threads but didn't,

Thanks ...

Well, my first response would be that partial differentiation is no different from ordinary differentiation, with the other variables taken to be literal constants.

But I have to ask: How well do you understand ordinary differentiation?
 
  • #3
Or do you mean 'integration by parts?'

- Warren
 
  • #4
Jeez, I didn't even notice that it said "integration". I saw "partial", and my brain just filled in the rest.

In that case, partial integration is usually taken to mean integration of a multivariable function over just one variable, with the others held constant.

So, Destroyer, is that what you mean, or do you mean integration by parts?
 
  • #5
integral of 3xcosx dx is the problem.


3xsinx - 3cos x + C should be the answer base on the table.
 
  • #6
Yes, ...

Yes I do understand Intergration and differentiation very well, i know how to get the derivative of anything, but because the integration is the opposite of differentiation, I'm getting some problems when trying to integrate some equation, especially I'm not in physics section, and i do need to make some researches on my own, hehehe
 
  • #7
I meant ...

I just mean i want everything you know about intergration, and i would be very thankful for that :)
 

1. What is partial integration?

Partial integration is a mathematical method used to solve integrals that involve the product of two functions. It involves breaking down the integral into simpler parts and then using a set of rules to solve it step-by-step.

2. Why do we need to use partial integration?

Partial integration is useful because it allows us to solve integrals that cannot be solved using traditional integration techniques. It is also helpful in simplifying complex integrals by breaking them down into smaller, more manageable parts.

3. What are the steps involved in partial integration?

The steps involved in partial integration are: 1) identifying the functions involved in the integral, 2) choosing which function to differentiate and which to integrate, 3) applying the product rule, 4) simplifying the resulting integral, and 5) repeating the process until the integral can be solved.

4. Can you provide an example of partial integration?

Yes, for example, consider the integral ∫ x cos(x) dx. We can use partial integration by differentiating x and integrating cos(x), which gives us ∫ x cos(x) dx = x sin(x) - ∫ sin(x) dx. This can be further simplified to ∫ x cos(x) dx = x sin(x) + cos(x) + C, where C is the constant of integration.

5. Are there any tips or tricks for mastering partial integration?

One helpful tip for mastering partial integration is to practice with various integrals and to become familiar with the product rule, which is a key step in the process. It can also be helpful to break down the integral into smaller parts, simplify as much as possible, and to double check your work for any mistakes.

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