# Rules and properties of integrals

Ok, this is the second step! I will cover the rules you need to apply to calculate an integral. With the next lesson, you will hopefully be able to start integrating! Let’s start! But first, I recommend you check out my post “What’s integration?” https://addjustabitofpi.com/2019/09/28/whats-integration/

*Linearity*

The sum or difference of two (or more) functions* under* the integral sign is equal to the sum or difference of the integral of each function.

Remember to use the parenthesis if you want to integrate a sum or a difference, because

makes no sense.

Also,

and more in general, whatever is not a function of the variable of integration, here x, is a constant and as such is taken out of the integral sign.

Example:

*Constant rule:*

Constants are taken out of the integration sign.

Example:

These rules are valid for definite integrals as well, but the latter have some other rules:

*Simmetry*

Examples of even function are x², cos(x), abs(x). It means that, whether the x is negative of positive, the result is going to be the same. In fact, 5²=(-5)²=25, cos(60) = cos(-60) = 0.5, abs(12) = abs(-12)=12 and so on.

Example:

Examples of odd functions are x^3, sin(x), x. It means that 2³ != (-2)³, in fact 8 != -8; sin(30) != sin(-30) (0.5 and -0.5) and so on.

*Continuous bounds*

Demonstration:

Example:

The following is a little introduction to integration techniques.

but I will talk about it in a more detailed way in the next post.

Once you memorise these rules and properties, it will be easier to understand how to actually calculate integrals. Wait for it!

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