#### Topics

##### Mathematical Logic

##### Mathematical Logic

##### Matrices

##### Differentiation

##### Applications of Derivatives

##### Integration

##### Definite Integration

##### Applications of Definite Integration

##### Differential Equation and Applications

##### Matrices

##### Commission, Brokerage and Discount

##### Insurance and Annuity

##### Linear Regression

##### Time Series

##### Index Numbers

- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number

##### Linear Programming

##### Assignment Problem and Sequencing

##### Probability Distributions

- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution

##### Continuity

##### Differentiation

##### Applications of Derivative

##### Indefinite Integration

##### Definite Integrals

##### Ratio, Proportion and Partnership

##### Commission, Brokerage and Discount

##### Insurance and Annuity

##### Demography

##### Bivariate Data and Correlation

##### Regression Analysis Introduction

##### Random Variable and Probability Distribution

##### Management Mathematics

#### notes

We consider the easy way of finding the area bounded by the curve y = f(x), x-axis and the ordinates x = a and x = b. Fig.

The area under the curve as composed of large number of very thin vertical strips. Consider an arbitrary strip of height y and width dx, then dA (area of the elementary strip)= ydx, where, y = f(x).

This area is called the elementary area which is located at an arbitrary position within the region which is specified by some value of x between a and b. The total area A of the region between x-axis, ordinates x = a, x = b and the curve y = f (x) as the result of adding up the elementary areas of thin strips across the region PQRSP. Symbolically, we express

A = `int_a^b dA = int_a^b ydx = int_a^b f(x) dx`

The area A of the region bounded by the curve x = g (y), y-axis and the lines y = c, y = d is given by

A = `int_c^d x dy = int_c^d g(y) dy`

we consider horizontal strips as shown in the following Fig.

**Remark:** If the position of the curve under consideration is below the x-axis, then since f (x) < 0 from x = a to x = b, as shown in following Fig .

The area bounded by the curve, x-axis and the ordinates x = a, x = b come out to be negative. But, it is only the numerical value of the area which is taken into consideration. Thus, if the area is negative, we take its absolute value, i.e., `|int_a^b f(x) dx|`.

Generally, it may happen that some portion of the curve is above x-axis and some is below the x-axis as shown in the following Fig .

Here , `A_1` < 0 and `A_2`> 0.Therefore, the area A bounded by the curve y = f (x), x-axis and the ordinates x = a and x = b is given by A = |`A_1`|+`A_2`.