Integral

Integration is the reverse operation of derivation.

The Integral of a function is the area under the function's graph.

Indefinite Integral Definition

When

Indefinite Integral Properties

Change of Integration Variable

When

								 and
								
								

Integration By Parts

Integrals Table

Definite Integral Definition

When

Definite Integral Calculation

When

								 ,
								
								

								 and


							


								
								

Definite Integral Properties

when

Change of Integration Variable

When

								 ,
								
								

								 ,
								
								

								 ,
								
								

Integration By Parts

Mean value theorem

When f(x) is continuous there is a point

								 so


							

Trapezoidal Approximation of Definite Integral

The Gamma Function

The Gamma function is convergent for x>0.

Gamma Function Properties

G(x+1)
				= xG(x)

G(n+1)
				= n!
				, 
									when
					n

![diagram](/math/calculus/integral.files/image115.gif)

ℕ 
									(positive integer).

The Beta Function

Beta Function and Gamma Function Relation