Integrating xy
What is Integration?
It is reverse process of differentiation. Refer to the flowchart for an overview of integrating a function.
When differentiating an expression any constant term dissappears. This means you can differentiate expressions with different constant terms (like x2 and x2+5) to give the same function. Therefore, after integrating an expression you must add an constant of integration at the end of the result. This is usually represented by the letter c
The formula to integrate expressions in the form xn is:
If f(x) notation is used, the following formula can be used:
To integrate expressions in the form kxn you integrate xn and multiply the integral by k. The following formulae, including f(x) notation to integrate an expression in the form in the form kxn:
Note: n can not be equal to -1 for any of this formulae, because as you need to divide the expression with the new power after you have added 1 to the power, you would be dividing by 0, which is undefined.
Example 1:
If you are integrating polynomials, apply the above formulae on to each term and add them together.
Example 2:
Practice Question:
