A-level Mathematics/MEI/C3/Integration

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Integration[edit | edit source]

Integration by Substitution[edit | edit source]


Integration by Parts[edit | edit source]


Integration by parts is used when you have two functions multiplied together, such as ln x and a simple polynomial, where 1 function is not the derivative of the other. As an example:

In this expression use the substitutions: and . In almost all other expressions, the polynomial is taken as u. After substituting, the expression in the example becomes:

After integrating and differentiating the respective parts of the expression, this becomes: