12.3 Integrals


• Integrals are often referred to as anti-derivatives


• definite integrals have boundaries defines. Indefinitie integrals do not have boundaries defines and a constant must be added to the result.


• To set up integrals use integration elements (aka slices),


• Some basic properties of indefinite integrals (no given start and end limits) include,



• Some of the trigonometric integrals are,



• Some other integrals of use that are basically functions of x are,




• Integrals using the natural logarithm base ‘e’,


12.3.1 Integration Examples


• Integration by parts - It is normal to have to do the integration by parts more than once to solve a problem.


• Substitution.


• Partial fractions can be used to reduce complex polynomials to simple to integrate forms.