NCERT Solutions for Class 10 Science Chapter 4

May 24, 202339 Insightful Publications

**NCERT Solutions for Maths Class 12 Exercise 7.8 Integrals**:** **The NCERT Solutions for Integrals Exercise 7.8 Class 12 Maths deals with the definite integral as the limit of a sum. This topic is essential to understanding what is known as a definite integral of a function. Students can learn more about the topic by solving the 6 practice questions in Exercise 7.8 Class 12 Maths. Students can check their basic understanding of the concept by solving the questions.

The Class 12 Maths NCERT Solutions Chapter 7 Integrals can be downloaded in PDF format from this page. To help students in improving their exam preparations, Embibe also provides free access to more than 6000 questions drawn from 41 different books. Scroll down to access the free NCERT Maths Class 12 Exercise 7.8 solutions.

Integrals is an important chapter that the students of Class 12 must practice. Practicing all these questions will help clarify the concepts and build a base for students. When the students understand the basics of Integrals in a proper manner, they will be able to resolve the questions for Maths in competitive exams easily.

Students can refer to the NCERT Solutions for Maths Class 12 Chapter 7 on Embibe to enhance their preparation and strengthen their understanding of Integrals. The study materials are available for free on Embibe, which will help students get better clarity of the subjects. Therefore, by practicing from these materials, they will be able to score higher marks in their exams.

Before going into the specifics of the NCERT solutions for Chapter 7, Integrals of the 12th-grade Math textbook, let us take a quick look at the topics covered in this chapter:

Exercise No. | Important Topics |
---|---|

7.1 | Integration as an Inverse Process of Differentiation |

7.2 | Methods of Integration |

7.3 | Integration by Partial Fractions |

7.4 | Integration by Parts |

7.5 | Definite Integral |

7.6 | Some Properties of Definite Integrals |

In order to help students in their test preparation, we have listed a few key concepts from NNCERT Solutions for Maths Class 12 Exercise 7.8 Integrals. Please note the following points:

**Integrals of the Form**∫px+qax2+bx+cdx∫px+qax2+bx+cdx:- Put px+q=lddx(ax2+bx+c)+m=l(2ax+b)+mpx+q=lddxax2+bx+c+m=l(2ax+b)+m, where ll and mm are determined by comparing coefficients on both sides.

**Integrals of the form**∫pcosx+qsinxacosx+bsinxdx:∫pcosx+qsinxacosx+bsinxdx:- Put p cos x+q sin x=l(a cosx+b sinx)+mddx(a cosx+b sinx)p cos x+q sin x=la cosx+b sinx+mddxa cosx+b sinx
- where
*l*and*mm*are constants to be found by solving the equations obtained by equating the corresponding coefficients of*sinxsinx*and cosxcosx on both sides.

**Integration by Parts:**- (i) ∫f1(x)⋅f2(x)dx=f1(x)∫f2(x)dx−∫[ddxf1(x)⋅∫f2(x)dx]dx∫f1x·f2xdx=f1x∫f2xdx-∫ddxf1x·∫f2xdxdx, where
*f1(x)f1x*is considered as the II function and f2(x)f2x as the IIII function. - We generally follow the rule ‘ILATE’ to determine which of the two functions is to be II and which of the two functions is to be the IIII.
- (ii) ∫ex[f(x)+f'(x)] dx=exf(x)+C

- (i) ∫f1(x)⋅f2(x)dx=f1(x)∫f2(x)dx−∫[ddxf1(x)⋅∫f2(x)dx]dx∫f1x·f2xdx=f1x∫f2xdx-∫ddxf1x·∫f2xdxdx, where
**Second fundamental Theorem of Integral Calculus:**- Let ϕ(x)ϕ(x) be the primitive or anti-derivative of a function f(x)f(x) defined on [a, b][a, b] i.e., ddxddx(ϕ(x))=f(x).(ϕ(x))=f(x). Then, ∫abf(x)dx=ϕ(b)−ϕ(a)

Students can go through the below list to get NCERT Solutions for all chapters of Class 12 Maths:

- 1st Chapter – Relations and Functions
- 2nd Chapter – Inverse Trigonometric Functions
- 3rd Chapter – Matrices
- 4th Chapter – Determinants
- 5th Chapter – Continuity and Differentiability
- 6th Chapter – Application of Derivatives
- 7th Chapter – Integrals
- 8th Chapter – Application of Integrals
- 9th Chapter – Differential Equations
- 10th Chapter – Vector Algebra
- 11th Chapter – Three Dimensional Geometry
- 12th Chapter – Linear Programming
- 13th Chapter – Probability

Students can check some frequently asked questions related to NCERT Solutions for Integrals Exercise 7.8 Class 12 Maths below:

**Ans**: There are a total of 11 exercises in the NCERT Solutions Class 12 Maths Chapter 7 Integrals. There are also miscellaneous questions based on the whole chapter that students can practice.

**Ans: **In NCERT Solutions Class 12 Maths Chapter 7 Exercise 7.8, students will learn about definite integral as the limit of a sum.

**Ans: **Students need to practice the questions given in the 11 exercises of Chapter 7 Integrals Class 12 Maths to solve questions in the final exam.

**Ans: **Yes, the NCERT textbooks and NCERT Solutions are the prescribed books for Class 12. These books are typically enough for the 12th-class board exam.

**Ans: **Students can download the NCERT Solutions exercise 7.8 Class 12 Maths Chapter 7 from this page. It can also be downloaded from the NCERT official website with the link given above or Embibe.com.

*We hope this detailed article on NCERT Solutions for Integrals Exercise 7.8 Class 12 Maths helps you prepare for the exam in the best way possible. For more updates on Class 12 exams, Stay tuned to Embibe.*