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.