Description:
Concepts of integration and its application to physical problems such as evaluation of areas, volumes of revolution, force, and work; fundamental formulas and various techniques of integration applied to both single variable and multi-variable functions; tracing of functions of two variables.
Overview:
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.
The integrals enumerated here are those termed definite integrals, which can be interpreted formally as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function. In this case, they are called indefinite integrals. The fundamental theorem of calculus relates definite integrals with differentiation and provides a method to compute the definite integral of a function when its antiderivative is known.
Read More:
(1) Introduction to Integration - Math is Fun
a. Anti-Differentiation
b. Indefinite Integrals
c. Simple Power Formula
d. Simple Trigonometric Functions
e. Logarithmic Function
f. Exponential Function
g. Inverse Trigonometric Functions
h. Hyperbolic Functions
i. General Power Formula
j. Constant of Integration
k. Definite Integral
2. Integration Techniques
a. Integration by Parts
b. Trigonometric Integrals
c. Trigonometric Substitution
d. Rational Functions
e. Rationalizing Substitution
3. Improper Integrals
4. Applications of Definite Integral
a. Plane Area
b. Areas Between Curves
5. Other Applications
a. Volumes
b. Work
c. Hydrostatic Pressure
6. Multiple Integral (Inversion of Order / Change of Coordinates)
a. Double Integrals
b. Triple Integrals
7. Surfaces Tracing
a. Planes
b. Spheres
c. Cylinders
d. Quadratic Surfaces
e. Intersection of Surfaces
8. Multiple Integral as Volume
a. Double Integrals
b. Triple Integrals
(1) Introduction to Integration - Math is Fun
by Don't Memorise [12:51] | YouTube
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Topics:
1. Integration Concept and Formulasa. Anti-Differentiation
b. Indefinite Integrals
c. Simple Power Formula
d. Simple Trigonometric Functions
e. Logarithmic Function
f. Exponential Function
g. Inverse Trigonometric Functions
h. Hyperbolic Functions
i. General Power Formula
j. Constant of Integration
k. Definite Integral
2. Integration Techniques
a. Integration by Parts
b. Trigonometric Integrals
c. Trigonometric Substitution
d. Rational Functions
e. Rationalizing Substitution
3. Improper Integrals
4. Applications of Definite Integral
a. Plane Area
b. Areas Between Curves
5. Other Applications
a. Volumes
b. Work
c. Hydrostatic Pressure
6. Multiple Integral (Inversion of Order / Change of Coordinates)
a. Double Integrals
b. Triple Integrals
7. Surfaces Tracing
a. Planes
b. Spheres
c. Cylinders
d. Quadratic Surfaces
e. Intersection of Surfaces
8. Multiple Integral as Volume
a. Double Integrals
b. Triple Integrals
PDF Materials (E-Books):
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