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JEE Maths
What is Integration in Maths

What is Integration in Maths? 

Integration is one of the most essential concepts in calculus, especially in Class 12 Maths and higher studies. It is essential in resolving problems related to areas, volumes, and accumulation of quantities. Integration is often referred to as the reverse process of differentiation.

In simple terms, integration is a mathematical technique to find the area under a curve or to accumulate quantities. It combines small parts to form a whole. It is commonly applied in physics, engineering, economics, and various real-life applications.

Mathematically, integration is the inverse operation of differentiation.

If dxd​F(x)=f(x)

then,

∫f(x)dx=F(x)+C

Where C is the constant of integration.

1.0Integration in Class 12 Maths

In Class 12 Maths, integration is a core chapter under Calculus. It includes:

  • Indefinite Integration: General integration without limits.
  • Definite Integration: Integration over a specific interval to find exact values.
  • Applications of Integrals: Finding areas bounded by curves.

2.0Types of Integrals

There are mainly two types of integrals in mathematics:

1. Indefinite Integrals:

Indefinite integrals represent a family of functions, and they include a constant of integration, C.

∫f(x)dx=F(x)+C

2. Definite Integrals:

These represent a fixed numerical value over a given interval [a, b]:

∫ab​f(x)dx

3.0Integration Calculus (Integral Calculus)

Integral calculus deals with finding integrals and solving problems involving:

  • Areas under curves
  • Volumes of solids of revolution
  • Accumulation of quantities
  • Motion and displacement problems

4.0Integral Calculus Formulas

Here are some basic integral calculus formulas frequently used:

Function

Integral

∫xndx

n+1xn+1​+C(for n=−1)

∫x1​dx

ln +C

∫exdx

ex+C

∫sinxdx

−cosx+C

∫cosxdx

sinx+C

5.0Fundamental Theorem of Integral Calculus

This theorem connects differentiation and integration:

dxd​(∫ax​f(t)dt)=f(x)

It states that integration and differentiation are inverse operations.

It also helps evaluate definite integrals easily:

∫ab​f(x)dx=F(b)−F(a)

Where F(x) is the antiderivative of f(x).

6.0Differential and Integral Calculus

Differential calculus focuses on finding the rate of change and slopes of curves using derivatives.
Integral calculus deals with the accumulation of quantities and area under curves through integrals.

Together, they form the two major branches of calculus:

  • Differential Calculus: Study of change.
  • Integral Calculus: Study of accumulation.

Table of Contents


  • 1.0Integration in Class 12 Maths
  • 2.0Types of Integrals
  • 3.0Integration Calculus (Integral Calculus)
  • 4.0Integral Calculus Formulas
  • 5.0Fundamental Theorem of Integral Calculus
  • 6.0Differential and Integral Calculus

Frequently Asked Questions

Integration is a mathematical process used to find the area under a curve, accumulate quantities, or reverse differentiation. It helps calculate areas, volumes, and more.

There are mainly two types of integration: Indefinite Integration: General integral with constant of integration (CC). Definite Integration: Calculates exact value over a specific interval [a,b][a, b].

Integration is crucial for solving problems related to: Areas under curves Volumes Motion problems Differential equations It is a scoring topic in Class 12 Maths and competitive exams like JEE.

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