Topics
Mathematical Logic
Matrices
Differentiation
Applications of Derivatives
Integration
Definite Integration
Applications of Definite Integration
- Standard Forms of Parabola and Their Shapes
- Ellipse and its Types
- Area Under Simple Curves
- Overview of Application of Definite Integration
Differential Equation and Applications
- Basic Concepts of Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Methods of Solving Differential Equations> Variable Separable Differential Equations
- Methods of Solving Differential Equations> Homogeneous Differential Equations
- Methods of Solving Differential Equations>Linear Differential Equations
- Applications of Differential Equation
- Overview of Differential Equations
Commission, Brokerage and Discount
- Commission and Brokerage Agent
- Concept of Discount
- Overview of Commission, Brokerage and Discount
Insurance and Annuity
- Insurance
- Types of Insurance
- Annuity
- Overview of Insurance and Annuity
Linear Regression
- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
- Overview: Linear Regression
Time Series
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend
- Overview of Time Series
Index Numbers
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Overview of Index Numbers
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
Assignment Problem and Sequencing
- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence
- Overview of Assignment Problem and Sequencing
Probability Distributions
Introduction
Integral calculus is a branch of mathematics that develops from two main ideas: finding a function when its derivative is known, and finding the area under a curve.
In simple words, differentiation tells how a quantity is changing, while integration helps recover the original quantity or measure the total accumulation of that quantity. The chapter introduces anti-derivatives, indefinite integrals, definite integrals, and the basic idea that these are connected through the Fundamental Theorem of Calculus.
Definition: Indefinite Integral
The collection of all anti-derivatives of a function is called its indefinite integral.
Here: f(x) = integrand, dx = variable of integration, C = constant of integration.
Definition: Definite Integral
A definite integral is connected with finding the area under a curve over a given interval. The chapter introduction presents area as one of the central motivating ideas behind integral calculus.
Key Points: Introduction of Integrals
- Primitive
Another name for anti-derivative. - Indefinite Integral
The family of all anti-derivatives of a function. - Definite Integral
An integral taken between two fixed limits, commonly used to represent area or total accumulation. - Integral Calculus
The branch of calculus dealing with anti-derivatives, accumulation, and areas under curves.
Video Tutorials
Shaalaa.com | Integration part 1
Series: series 2
00:35:26 undefined
00:40:02 undefined
00:36:20 undefined
00:30:56 undefined
00:30:15 undefined
00:34:58 undefined
00:35:00 undefined
00:24:04 undefined
00:26:20 undefined
00:30:15 undefined
00:30:14 undefined
