Firstly it is not integra...it is integer...
All natural numbers with its negative included 0 is called integers.ex-1,2,3,-1,-2,-3,0etc

Integers and Operations

Integers are whole numbers that are either positive, negative or zero. They do not include fractions or decimals. Integers can be added, subtracted, multiplied or divided just like any other numbers. The basic operations of integers are:

1. Addition: When two integers are added, we get a sum. If both integers have the same sign, we add their absolute values and keep the same sign. If they have opposite signs, we subtract their absolute values and keep the sign of the larger number.

2. Subtraction: When we subtract one integer from another, we get the difference. To subtract one integer from another, we add the opposite of the second integer.

3. Multiplication: When two integers are multiplied, we get a product. The sign of the product is positive if both integers have the same sign, and negative if they have opposite signs.

4. Division: When we divide one integer by another, we get a quotient. Division of integers is similar to division of whole numbers. We have to be careful when dividing by zero, as division by zero is undefined.

Integrals

An integral is a mathematical concept that is used to find the area under a curve. Integrals are used in calculus, which is a branch of mathematics that deals with change and motion. Integrals are represented by the symbol ∫ and have limits of integration, which are the values at which we start and end the integration.

Types of Integrals

1. Definite Integral: A definite integral has limits of integration and gives a specific value.

2. Indefinite Integral: An indefinite integral does not have limits of integration and gives a family of functions.

Applications of Integrals

Integrals have several applications in science and engineering. Some of the applications of integrals are:

1. To find the area under a curve.

2. To calculate the velocity and acceleration of an object.

3. To calculate the volume of a solid.

4. To find the average value of a function.

Conclusion

Integers and operations are essential in mathematics, and integrals are used in advanced mathematics. Understanding the basics of integers and operations is crucial for solving problems in mathematics. Integrals have several applications in science and engineering, and they are used to find the area under a curve, calculate the velocity and acceleration of an object, find the volume of a solid, and find the average value of a function.