Class 12th Math Application of Integrals NCERT Solution CBSE 2023
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NCERT Solutions for Class 12 Maths Chapter 8

Chapter 8 Application of Integrals

The application of integrals are used in the construction of buildings or for determining the length of power cables needed to connect two substations. Students must thoroughly review the chapter’s topics before and then answer the exercise questions. 

In this article, we have provided NCER notes for Chapter 8 prepared by our experts to help students answer the questions efficiently. Students can easily go through the solutions and clear their concepts.


Points to Remember

Below we have provided some of the important points to remember for this chapter to ace the exams:

  • Integrals are of two types; one is Indefinite Integrals, and the other is Definite Integrals.

  • Indefinite integrals do not have any limits, such as upper and lower bounds. Indefinite integrals use to integrate algebraic expressions, trigonometric functions, logarithmic functions, inverse trigonometric functions, and exponential functions.

  • Definite integrals calculate the area of a curve in a graph within boundaries, such as the lower and upper limits. They can be written as [a,b] to calculate the area of the f(x) curve concerning the x-axis.

  • The definite integral between two points is used to calculate the area under the curve between two points.

  • The area between two curves is the area between two intersecting curves, which can be calculated using integration.

  • Application of Integrals can be used in various fields, including mathematics, physics, and engineering.

Topics and Sub-topics

Before getting into the details of NCERT notes for 12th-grade Math's Chapter 7 Integrals, let us have an overview of the list of topics included in this chapter:

Topic Name

Topic Name

Integration as an Inverse Process of Differentiation

Integration by Parts

Methods of Integration

Definite Integral

Integration by Partial Fractions

Some Properties of Definite Integrals


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