Integration of polynomial functions
Let's start by going through different functions and looking at rules for their integration. Let's start with the integral rule of the power function:
The result is generally valid whenever the original function is defined. However, at this stage, let us consider only the situation where r = 1,2,3,4,…. that is, r is a positive integer. [Check this rule yourself by deriving the expression to the right of the equation!].
If the function has no variable at all (the power of x is zero), a simpler memory rule can be used
Combined with the integral rule of the sum mentioned in the previous chapter, we can now calculate the integrals of polynomial functions.
Example 1: Integrate
The rules should be used as much as possible before integrating separate terms, often the expression to be integrated is significantly simplified and there is less to be calculated.
Example 2: Find the integral
In addition, it is worth noting that if there is a parentheses expression inside the integral, it must first be opened before the integral can be calculated.
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