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AS/A-Level Mathematics - Intro to Integration

Intro to Integration

· A-Level Maths,calculus,function,Differentiation,integration

Integration is a way of adding  slices to find the whole. Let's learn about it in A-Level Maths.

Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start   with finding the area between a function and the x-axis like this:

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Finding an Integral is the  reverse of finding a derivative.

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Notation  

The symbol for "Integral" is a stylish "S" (for "Sum", the  idea of summing  slices):

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After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width).

And here is how we write the answer:

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Plus C

It is  the "Constant of Integration". It  is there because of  all the  functions whose derivative is 2x:

  • the derivative of x2 is 2x, 
  • and the derivative of x2+4 is also 2x, 
  • and the derivative of x2+99 is also 2x, 
  • and so on! 

Because the derivative of a constant is zero.

So when we reverse the operation (to find the integral) we only know 2x, but there could have been a constant of any value.

So we wrap up the idea by just writing + C at the end.

Definite vs Indefinite Integrals 

A Definite Integral has actual values to calculate between (they are put at the bottom and top of the "S"):

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Drafted by Eunice (Maths)

Reference

https://www.mathsisfun.com/calculus/integration-introduction.html

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