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Integration in Maths – Definition, Formulas and Types, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives. Integration is one of the two major calculus topics in mathematics, apart from differentiation(which measure the rate of change of any function with respect to its variables). It’s a vast topic which is discussed at higher level classes like in class 11 and 12. Integration by parts and by the substitution is explained broadly. Here, you will learn the definition of integrals in maths, formulas of integration along with examples.

Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, …

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Integral Calculus – Definition, Formulas, Methods, Applications, Examples, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
Integral calculus is the branch of calculus where we study integrals and their properties. Integration is an essential concept which is the inverse process of differentiation. Both the integral and differential calculus are related to each other by the fundamental theorem of calculus. In this article, you will learn what is integral calculus, why it is used, its types, formulas, examples, and applications of integral calculus in detail.

Integral Calculus is the branch of calculus where we study integrals and their properties. Integration is an essential concept which …

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Differential Calculus & Approximation | Tangent Line Approximation, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
In mathematics, differential calculus is a branch of mathematics that deals with the process of finding the derivative of a function. It is the study of the rate of change of quantities with respect to other variables.

In mathematics, differential calculus is a branch of mathematics that deals with the process of finding the derivative of a …

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Equation of Tangent And Normal to a Curve with Examples, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
The applications of derivatives are:

The applications of derivatives are: In this article, we will learn to use differentiation to find the equation of the tangent …

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Increasing & Decreasing Functions Monotonicity with Examples for Functions, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
Before explaining the increasing and decreasing function along with monotonicity, let us understand what functions are. A function is basically a relation between input and output such that, each input is related to exactly one output.

Before explaining the increasing and decreasing function along with monotonicity, let us understand what functions are. A function is basically a …

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Mean Value Theorem Formula Equation | Mean Value Theorem For Integrals, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
In mathematics, the mean value theorem states, roughly, that given a planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

In mathematics, the mean value theorem states, roughly, that given a planar arc between two endpoints, there is at least …

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Second Order Derivative | Explanation with Examples, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
For understanding the second-order derivative, let us step back a bit and understand what a first derivative is. The first derivative dy/dx represents the rate of the change in y with respect to x. Considering an example, if the distance covered by a car in 10 seconds is 60 meters, then the speed is the first order derivative of the distance travelled with respect to time. Hence, the speed in this case is given as 60/10 m/s.

For understanding the second-order derivative, let us step back a bit and understand what a first derivative is. The first …

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Derivatives Of A Function In Parametric Form-Solved Examples, Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
Derivatives of a function in parametric form: there are instances when rather than defining a function explicitly or implicitly we define it using a third variable. This representation when a function y(x)  is represented via a third variable which is known as the parameter is a parametric form. A relation between x and y can be expressible in the form x = f(t) and y = g(t) is a parametric form representation with parameter as t. Now we will concentrate on how to differentiate these functions using parametric differentiation.

Derivatives of a function in parametric form: There are instances when rather than defining a function explicitly or implicitly we …

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Matrices Exercise 3.3 NCERT Solutions Class 12 Math Chapter 3 free PDF Download

September 1, 2025January 8, 2025 by Neeraj Anand, Param Anand
Chapter 3 of the class 12 ncert mathematics textbook, titled “matrices,” delves into the fundamental concepts of matrices, including their types, operations, and applications. Exercise 3. 3 focuses on practical problems involving matrix operations, such as addition, subtraction, and multiplication of matrices. This exercise helps students apply their understanding of matrices to solve various mathematical problems.

Chapter 3 of the Class 12 NCERT Mathematics textbook, titled “Matrices,” delves into the fundamental concepts of matrices, including their …

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Matrices Exercise 3.2 NCERT Solutions Class 12 Math Chapter 3 free PDF Download

January 8, 2025 by Neeraj Anand, Param Anand
Matrices are a fundamental concept in linear algebra, used extensively in mathematics, physics, engineering, computer science, and various other fields. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The numbers or elements inside a matrix are enclosed within square brackets and can be used to represent systems of linear equations, transformations, and many real-world data structures. Operations such as addition, subtraction, multiplication, and finding determinants and inverses of matrices help solve complex mathematical problems efficiently.

Matrices are a fundamental concept in linear algebra, used extensively in mathematics, physics, engineering, computer science, and various other fields. …

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Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Miscellaneous Exercise Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

NCERT Solutions Probability Miscellaneous Exercise Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

NCERT Solutions Probability Exercise 13.3 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.3 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.2 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.2 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.1 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.1 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Chapter 11 Three Dimensional Geometry from Anand Classes. Clear, step-by-step maths notes in PDF format.

Three Dimensional Geometry NCERT Solutions Miscellaneous Exercise Chapter-11 Class 12 Math Notes PDF Free Download

Download free NCERT Solutions for Class 12 Chapter 11 Three Dimensional Geometry from Anand Classes. Clear, step-by-step maths notes in PDF format.

Three Dimensional Geometry NCERT Solutions Exercise 11.2 Chapter-11 Class 12 Math Notes PDF Free Download (Set-2)

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