Learn why we get the area of a function by integrate it

In summary, the conversation was about the integration of a function and how it relates to finding the area under the curve. The speaker shared a helpful tutorial on the subject and encouraged those who are struggling with understanding integration to use it as a resource. They also mentioned a related article and suggested asking for further clarification in a Calculus Forum.
  • #1
unseensoul
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For those who want to understand why the integration of a function gives the area of it, you can take a look at...

http://www.mathsroom.co.uk/downloads/Integration-Area_Under_A_Curve.ppt"

I'm posting this because I think that not everyone who makes use of integration can really understand it. However, as it was very difficult to me to find such a good tutorial covering that aspect so well and clear, I am sharing it with those who are also interested in.
 
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What is integration?

Integration is a mathematical process that involves finding the area under a curve on a graph. It is represented by the symbol ∫ and is the reverse operation of differentiation.

Why do we get the area of a function by integrating it?

We get the area of a function by integrating it because integration allows us to calculate the total area under the curve of a function. This is useful in many applications, such as calculating the displacement of an object or the total cost of a production process.

How does integration work?

Integration involves breaking down a function into smaller parts and calculating the area under each part. This is done by using a technique called Riemann sums, where the area is approximated by rectangles. As the number of rectangles increases, the approximation becomes more accurate, and the total area can be calculated.

What are the different types of integration?

There are two main types of integration: indefinite and definite. Indefinite integration involves finding the general antiderivative of a function, while definite integration involves calculating the area under a specific part of a function, within a given interval.

What are the applications of integration?

Integration has many real-world applications, such as calculating the displacement of an object, finding the total cost of a production process, and determining the volume of irregular shapes. It is also used in physics, engineering, economics, and many other fields.

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