Trigonometric Functions
Trigonometric Functions:
If u is a function x, where u' dx = du, then
ò sin u du = -cos u + C
Calculus
Forum reference:
Book page:
http://course-notes.org/Calculus
Approximate Integration- Trapezoidal and Simpson's Rule
Approximate Integration- Trapezoidal and Simpson's Rule
In order to evaluate 
, the interval [a,b] is subdivided into n subintervals
each of length:
Area Between Two Curves
Area Between Two Curves:
The formula for finding the area between two curves is:
where f(x) and g(x) are graph of curves, a and b are the intersection points of the two curves.
Indefinite Integrals
Indefinite Integrals:
The indefinite integral of a function f, denoted as ò f(x) dx, is the set of all the antiderivatives of f.
Properties of Indefinite Integrals:
Area under a Curve using Definite Integrals
Area under a Curve using Definite Integrals:
The area of the region bounded by the graph of the function f the x-axis and two vertical lines x = a and x = b; is:
Definite Integrals
Definite Integrals:
Definite Integrals are defined as:
and also:
Integration
Integration
The integral of a function f, denoted as ò f(x) dx = F(x) + C, where C is an arbitrary constant number, is an antiderivative of the function F, that is, F '(x) = f(x) for all x in the domain of f.
Area Under a Curve
Area Under a Curve:
Properties of Areas:
  1. Given any region R, then the area, A(R) is a real number;
     A(R) ³ 0.
  2. Given two congruent regions, then their areas are equal.
  3. If R = R1 E` R2 ,where R1 and R2 have only boundary points in common, then A(R1) + A(R2) = A(R).
Sigma Notation
Sigma Notation
Sigma Notation is a notation used to abbreviate long summations of a given expression.
ex.
Antiderivatives
Antiderivatives
Given a function F is called an antiderivative of the function f if for all x in the domain of f that F '(x) = f(x) + C, where C is any constant.
ex.
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