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==Definite Integrals==

A definite integral is the area under the curve between two points on the function. In the picture below, the yellow area is "positive" and the blue area is "negative". The integral is evaluated by adding the positive area together and subtracting the negative area.

If the function f(x) is real rather than complex, then the definite integral is also known as a Riemann integral.

== Solving Definite Integrals ==

Solving a definite integral usually has two main steps: [[integration]] and [[subtraction]].

== Example 1==

: <math>F(5) = {1 \over 3}5^3 = {125 \over 3}</math>

: <math>F(-3) = {1 \over 3}(-3)^3 = {-27 \over 3}</math>

: <math>{125 \over 3} - {-27 \over 3} = {125 \over 3} + {27 \over 3} </math>

: <math>= {152 \over 3}</math>

: <math>\int_4^{12}\frac{3x+11}{x^2-x-6}dx </math>

=== Integration ===

<br />As shown on the page mentioned above:

: <math>\int\frac{3x+11}{x^2-x-6}dx=4ln|x-3|-ln|x+2|+c</math>