NCERT Solutions Class 12 Maths Chapter 8 Miscellaneous Exercise

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.

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.

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.