What is Integration? Help Understanding Symbols & Process

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    Integration
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Discussion Overview

The discussion centers around the concept of integration, particularly in the context of finding the area under a curve, as introduced in a lecture. Participants explore the symbols and processes involved in integration, addressing the confusion of a newcomer to the topic.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about integration, having never encountered it before and seeking help with the symbols and process.
  • Another participant suggests that integration is the process of adding infinitely small pieces together to form a whole, noting this is not a mathematically rigorous definition.
  • Some participants question the appropriateness of the course level for the original poster, suggesting they should confirm their understanding of prerequisites and whether integration has been covered in prior lectures.
  • Integration is described by some as a form of 'big-boy' addition or multiplication, relating it to finding areas, volumes, and other quantities through the accumulation of smaller parts.
  • One participant mentions that integration is the opposite of differentiation, providing examples of how integration relates to distance, speed, and area.
  • There is a discussion about the symbols used in integration, with some participants asserting that they are straightforward when broken down individually.
  • Another participant describes integration as a limit of a summation as it approaches a number, while another elaborates on the concept of summing infinite thin polygons defined by a function.

Areas of Agreement / Disagreement

Participants express a range of views on the definition and understanding of integration, with no consensus reached on a singular explanation or approach. Some participants agree on basic concepts, while others raise questions about course prerequisites and the clarity of instruction.

Contextual Notes

There are indications that some participants may have differing levels of familiarity with calculus concepts, which could affect their understanding of integration. The discussion reflects varying interpretations of integration and its symbols, highlighting the need for foundational knowledge in calculus.

Who May Find This Useful

This discussion may be useful for students new to calculus or those seeking clarification on the concept of integration and its applications in mathematics.

mathman100
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ok, so in one of my lectures our prof. showed us a graph, (that pretty much looked like an upside down parabola.) We had to find the area under the curve, and she told us we had to use integration. I'd never even heard of it before, and I don't understand what all the symbols mean, or how to use them. Can anyone help me out?
 
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You need to learn some calculus, start frequenting the math forum. In a very modest, brief definition, integration is the process of adding infinitely small pieces togther to make a whole.(NOT THE MATHMATICALLY RIGOROUS DEFINITION FOR SURE!) Integration can be used to find the area under a curve.
 
mathman100 said:
ok, so in one of my lectures our prof. showed us a graph, (that pretty much looked like an upside down parabola.) We had to find the area under the curve, and she told us we had to use integration. I'd never even heard of it before, and I don't understand what all the symbols mean, or how to use them. Can anyone help me out?

What class is it for? That's really odd that a teacher would be like, "use integration to find the area under the graph" when you've never done it before.

Unless she was going to be explaining what integration was? that would make more sense.

You should ask her what integration is. Everyone else in the class is probably where you are at.
 
http://en.wikipedia.org/wiki/Integral

What do you know? Have you learned differential calculus (how to find derivatives, etc.)? Did you miss any lectures in which integration may have been explained? Do you have all the prerequisites for this course (and are you sure you're in the right course?!)?

Essentially, there are two branches to calculus, integral calculus and differential calculus. Differential calculus deals with differentiation, and integral calculus deals with antidifferentiation.

You also undoubtedly have a textbook assigned for this course. In addition to asking your instructor to explain things, you should probably take a look at it! It'll undoubtedly explain integration, though it's very strange that you're in a course where your instructor assumes knowledge of integral calculus and you've never heard of it before (especially if, as I'd guess, this is a first-year university course? They should know what you're expected to have learned already!).
 
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Integration is just 'big-boy' addition.
 
Plastic Photon said:
Integration is just 'big-boy' addition.

Or multiplication, because it's repeated addition and turns distance into area, area into volume, etc.
 
basically it's opposite of derivation. in slang it'd be defined as "kicking an equation up to the next level"

it's like getting distance traveled if you know speed...or getting speed if you know acceleration. Or getting area if you know perimeter...or volume if you know area.

in plain math, it's finding area between the x-axis and the curve you're looking at over a closed interval...and it's the opposite operation than derivation. Yes it's the super-steroids version of an addition in a way.

the symbols are pretty simple if you look at them 1 by 1.

[tex]\int[/tex] is just the symbol of operation. the lower and upper numbers tell you between what values of x you do this operation...and the dy/dx or dx...just is, and does nothing but make the operation possible (it's easier to put it that way even if some smart people will trow rotten tomatoes at me for saying that).
 
It's basically the limit as a summation approaches a number right?
 
Yep, summation of an infinite number of infinitely thin polygons whose length is defined by the value of the function at that point.
 
  • #10
To the OP: if it's a new course, and you haven't heard of integration, I'd be worried what other prerequisites you don't know about...
 

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