Revision Notes for CBSE Class 12 Maths Chapter 7 (Integrals) - Free PDF Download
FAQs on Integrals Class 12 Notes CBSE Maths Chapter 7 (Free PDF Download)
1. How would you solve integrals of trigonometric formulas like; ∫dx/y + z Cos(x)
The working rule for solving such integrals is:
In place of Cos(x) put (1 - tan2 x/2)/(1 + tan2x/2) and for Sin x replace with (2tan x/2)/(1 + tan2 x/2). This is done so that the integrand becomes a function of tan x/2.
Now replace tan x/2 with ½ Sec2 x/2 dx = dz
Now integrate the rational algebraic function of z
In the result replace z with tan x/2
2. What is the difference between a definite integral and an indefinite integral?
In an indefinite integral there are no limits of integration whereas a definite integral is bound by lower and upper limits which are constant.
A Definite Integral is denoted as - ∫ab f(x), Here a and b are constants.
An Indefinite Integral is denoted as - ∫f(x)
3. What are the important questions for Chapter 7 of Class 12 Maths?
Chapter 7 of Class 12 Maths is an important Chapter in terms of your final board examination as well as for other competitive exams. This Chapter explains the concept of Integration, which includes integral calculus and its properties. There are many important questions in this Chapter that come from very important concepts and topics. These include evaluation of integrals, determination of integrals, functions of integrals, anti-derivatives, and various methods of integrations.
4. Where can I find revision notes for Chapter 7 of Class 12 Maths?
The board question papers generally rely on NCERT textbooks and the concepts it covers. Therefore, studying from NCERT textbooks can ensure that you will score good marks. For Chapter 7 of Class 12 Maths, you can revise notes based on NCERT Solutions on Vedantu. It provides all important questions and solutions. These solutions and questions are extremely important for all CBSE students from the viewpoint of examinations. Also, the solutions PDF is available for free download on the Vedantu mobile app.
5. How can I score well in Chapter 7 of Class 12 Maths?
To score well in Chapter 7 of Class 12 Maths, you need to keep practising. You need to have a personal notebook where you can write all the notes. This will help you to remember the concepts and topics that you learned. This will help you prepare thoroughly, and it will ensure that you don’t forget all the important concepts and topics you learned. It will cater you with knowledge and a better understanding of the subject. Making notes will also be helpful during your revision time.
6. What are the basics of integration, according to Chapter 7 of Class 12 Maths?
Chapter 7 “Integrals” of Class 12 Maths is an easy chapter and will help you score good marks. Integration refers to the addition of parts to find the whole. This technique is used to find volumes, areas, and so on. This technique is a mathematical inverse of differentiation. There are many important formulas in this chapter that you must learn and understand for you to know the basics of this chapter. Apart from this, you must understand the different types of methods in Integration. The students can also refer to the Revision Notes for Chapter 7 of Class 12 Maths free of cost from the Vedantu website or from the Vedantu app.
7. What are the properties of Indefinite Integral, according to Chapter 7 of Class 12 Maths?
Indefinite Integral is the function that uses another function's antiderivative function. Some of the properties include:
In an Indefinite Integral, the integrand and the derivative are equal to each other.
The Indefinite Integral of the sums of two functions equals the integral of the sums of two functions.
The difference between the two functions of indefinite integrals is equal to that of the two functions.
An integral always has a constant, which can be moved outside of the integration.