NCERT Solutions for Class 12 Maths Chapter 8 Miscellaneous Exercise of Application of Integrals (Area bounded) in English and Hindi Medium. The questions of 12th Maths misc. ex. 8 are updated as per the rationalised syllabus and new NCERT textbook issued for CBSE 2024-25.

## 12th Maths Chapter 8 Miscellaneous Exercise in Hindi and English

### Class 12 Maths Chapter 8 Miscellaneous Exercise Solution

Class XII Mathematics Chapter 8 Miscellaneous Exercise solutions free to use updated for academic session 2024-25. These solutions are useful for all the students studying in CBSE, UP Board, MP Board or other state board following NCERT Textbooks for grade 12. Solutions are available in PDF as well as videos format free to use online or download without any login or registration.

Class: 12 | Mathematics |

Chapter: 8 | Miscellaneous Exercise 8 |

Chapter Name: | Application of Integrals |

Content: | Exercise Solution Extra Questions |

Content Mode: | Text and Videos Format |

Session: | Academic Year 2024-25 |

Medium: | English and Hindi Medium |

#### Class 12 Maths Chapter 8 Miscellaneous in Videos

##### 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 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?

Earlier there were total of 19 questions in all. Out of which last four questions are multiple choice questions. But as per the rationalised syllabus for new session, there are only 5 questions in which last two are multiple choice questions.

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

Question number 1, 2, and 5 are little bit tricky as well as important for exams. Practice these question paying more attention.