CBSE NCERT Solutions for Class 12 Maths Chapter 7 Integrals: Engineering aspirants and students appearing for CBSE Class 12 board exams must take the NCERT Mathematics textbooks seriously and finish them from top to bottom. They must also go through the NCERT solutions for Class 12 Maths Chapter 7 to have a better understanding of the various concepts.
In this article, we will provide you with NCERT Solutions for Class 12 Maths Chapter 7 – Integrals which have been designed by the best teachers in India. Read on to find out everything about CBSE NCERT Solutions for Class 12 Maths Chapter 7 Integrals.
NCERT Solutions for Class 12 Maths Chapter 7 PDF
Before getting into the details of NCERT Solutions for Class 12 Maths Chapter 7 Integrals, let’s have an overview of the list of topics and sub-topics under this chapter.
|2||Integration as an Inverse Process of Differentiation|
|3||Geometrical interpretation of indefinite integral|
|4||Some properties of indefinite integral|
|5||Comparison between differentiation and integration|
|6||Methods of Integration|
|7||Integration by substitution|
|8||Integration using trigonometric identities|
|9||Integrals of Some Particular Functions|
|10||Integration by Partial Fractions|
|11||Integration by Parts|
|12||Integral of the type|
|13||Integrals of some more types|
|15||Definite integral as the limit of a sum|
|16||Fundamental Theorem of Calculus|
|18||First fundamental theorem of integral calculus|
|19||Second fundamental theorem of integral calculus|
|20||Evaluation of Definite Integrals by Substitution|
|21||Some Properties of Definite Integrals|
Download NCERT Solutions For Class 12 Maths Chapter 7 Integrals PDF
NCERT Solutions for Class 12 Maths Chapter 7 Integrals contains step-by-step and detailed solutions for every question. Students can also download the NCERT Solutions for Class 12 Maths Chapter 7 Integrals PDF to study in offline mode as well.
NCERT Solutions For Class 12 Maths Chapter 7 – Integrals NCERT Solutions
Differential Calculus is centred on the concept of the derivative. The original motivation for the derivative was the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines. Integral Calculus is motivated by the problem of defining and calculating the area of the region bounded by the graph of the functions.
The functions that could possibly have given function as a derivative are called anti derivatives (or primitive) of the function. Further, the formula that gives all these anti derivatives is called the indefinite integral of the function and such process of finding anti derivatives is called integration. Such type of problems arise in many practical situations. For instance, if we know the instantaneous velocity of an object at any instant, then there arises a natural question, i.e., can we determine the position of the object at any instant? There are several such practical and theoretical situations where the process of integration is involved. The development of integral calculus arises out of the efforts of solving the problems of the following types:
(a) the problem of finding a function whenever its derivative is given
(b) the problem of finding the area bounded by the graph of a function under certain conditions. These two problems lead to the two forms of the integrals, e.g., indefinite and definite integrals, which together constitute the Integral Calculus.
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