# NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise of Application of Integrals (Area bounded) in English Medium as well as Hindi Medium free to use updated for academic session 2021-2022.

These solutions are useful for all the students studying in CBSE, UP Board, MP Board or other state board following NCERT Textbooks. Solutions are available in PDF as well as videos format free to use online or download without any login or registration.

## Class 12 Maths Chapter 8 Miscellaneous Exercise Solution

• ### NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise

 Class: 12 Mathematics Chapter: 8 Miscellaneous Exercise 8 Contents: NCERT Solutions in Hindi and English Medium

### Class 12 Maths Chapter 8 Miscellaneous in Videos

Class 12 Maths Chapter 8 Miscellaneous in English
Class 12 Maths Chapter 8 Miscellaneous in Hindi

#### History of Integral Calculus

Integral calculus has its origins in the early stages of the development of mathematics and is related to the exhaustion method developed by ancient Greece’s mathematicians. This method originated in solving problems on the calculation of plane figures, surface areas and volume of solid bodies, etc. In this sense, the depreciation method can be considered as an initial method of integration.

The most significant development of the exhaustion method in the early period was achieved in the works of Eudoxus (440 BCE) and Archimedes (300 BCE). In conclusion, the basic concepts and theory of integral calculus and it’s mainly with differential calculus relationships were developed at the end of the 17th-century, I. Newton, and G. In Leibnitz’s work.

##### How to plot a rough figure for calculating area

We just solve all the given curves and get the intersection points corresponding to each curve. First of all just plot the points. Now, consider all the curves one by one. First of all plot the line if any then the next curves. During the plotting, must consider the common intersecting points of each curve.

##### How many important examples are there in Class 12 Maths Chapter 8 Miscellaneous Exercise?

There are total five examples in CBSE 12th Maths Miscellaneous exercise 8 but the fifth example (Example number 14) is considered as the most important example. It is frequently asked in school exams as well as CBSE board.

##### How many questions are there in Class 12 Maths Miscellaneous Exercise 8?

There are total of 19 questions in all. Out of which last four questions are multiple choice questions.

##### Which questions is the most important questions in Miscellaneous Exercise 8 of Class 12 Maths?

Question number 4, 7, 10 and 11 are little bit tricky as well as important for exams. Practice these question paying more attention.

##### Is there always a question in CBSE board exams from misc. ex. 8 of class 12 Maths?

There may be questions from any of exercises not necessarily from miscellaneous exercise 8.                       