The title would be Understanding Integrals: A Basic Breakdown

In summary, the conversation is discussing integrals and their basic concepts. One person is asking for a breakdown of integrals and another person is providing an informal reference, but also emphasizing the importance of studying from textbooks for a proper understanding. The conversation also touches on recognizing when to use different techniques for integration. A link to a tutorial on integrals is provided.
  • #1
kevinlikesphysics
57
0

Homework Statement



Can someone give me a very basic breakdown of integrals i read the manual in the tutorials sections and i just don't understand what equations have to be used for each part.

Homework Equations





The Attempt at a Solution

 
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  • #2
The integral is the anti-derivative of a function. The derivative of 2x would be 2. Then the anti-derivative (integral) of 2 would be 2x + C where C = 0. (boundary or initial conditions have to be told to you for definite integrals).
 
  • #3
No offence to any of the authors, but those introductory tutorials are really no where near as good as a proper introduction to these concepts found in decent textbooks. There are no quick fixes.
 
  • #4
I take it that was mine. That was meant as an informal reference and not something to be learned from by itself. It does assume a moderate standard of mathematical knowledge before hand.

If you could define what is troubling you exactly it might be easier to help. Specifically, what do you mean by 'what equations have to be used for each part'? If you're asking how do you recognise when to use integration by substitution over integration by parts then the answer is it just takes practise. Do as many problems as possible and you will soon recognise when one technique will work over another.
 
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  • #5
Kurdt said:
I take it that was mine. That was meant as an informal reference and not something to be learned from by itself. it does assume a moderate standard of mathematical knowledge before hand.

Yes I did mean yours Kurdt =] And yes I knew myself that you meant it as an informal reference, but many students look for things like this expecting to see a quick route to understanding that they just won't get with that sort of attitude. Your contribution, however, fulfills its intended purposely excellently, i have nothing to lower it =].
 
  • #6
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  • #7
Schrodinger's Dog said:
Aren't there some excellent tutorials on integrals in the Learning & resources/ er forget the name section hold on Maths and science learning materials?

https://www.physicsforums.com/showthread.php?t=213784

Nicely done Kurdt very well presented.

I think that's perhaps the 'manual' the OP was referring to.
 
  • #8
Kurdt said:
I think that's perhaps the 'manual' the OP was referring to.

I know, thus the edit. :smile:

Thats' what happens when you read only the op post, and then the rest in reverse order. :biggrin:
 

1. What is a general integral question?

A general integral question is a type of mathematical question that involves finding the area under a curve. It typically involves an equation with an unknown variable and requires solving for that variable using integration techniques.

2. How is a general integral question different from a regular integral question?

A general integral question is different from a regular integral question because it does not have specific limits of integration and instead requires solving for the variable in the equation. Regular integral questions have specific limits of integration and require finding the definite integral.

3. What are some common methods for solving general integral questions?

Some common methods for solving general integral questions include substitution, integration by parts, and partial fractions. These methods involve manipulating the equation to simplify it and then using integration rules to find the solution.

4. Can general integral questions be solved using a calculator?

Yes, general integral questions can be solved using a graphing calculator or integration software. However, it is important to understand the concepts and techniques behind solving these questions in order to use the calculator effectively.

5. How can I check my answer for a general integral question?

You can check your answer for a general integral question by taking the derivative of the solution and comparing it to the original equation. If they are equal, then your solution is correct. You can also use online integral calculators to verify your answer.

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