NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.10 Integrals

NCERT Solutions for Class 12 Maths Exercise 7.10 Integrals: Chapter 7 of class 12 deals with an important topic called Integrals. To score great marks, one has to go through the NCERT exercises and solutions thoroughly before the exams. NCERT Solutions for Integrals Exercise 7.10 Class 12 Maths will assist students in checking answers once they have completed chapter 7 Maths class 12 exercise questions.

Embibe’s NCERT Solutions for Ex 7.10 class 12 is created by subject matter experts and is based on the latest CBSE guidelines. Ex 7.10 class 12 PDF is available in this article. Continue reading this article to get NCERT solutions for exercise 7.10 class 12th maths. 

NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.10: Important Topics

The NCERT Solutions for Class 12 Maths exercise 7.10 covers the concept of Evaluation of Definite Integrals by Substitution. In this section, students will learn methods for finding the indefinite integral by the method of substitution. Students can follow the conceptual videos of Embibe to gain command on the topics before moving to problem-solving.

Embibe offers 3D interactive videos while making learning fun for students. Besides these videos, students can also use Embibe books, Exemplars, and other content for. If students wish to score good marks, they can start practicing through the Embibe 3D and Exemplar videos.

Below are the important concepts in NCERT ex 7.10 Class 12 Maths Integrals:

NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.10: Points To Remember

Students can refer to a few points to remember for better clarity of the chapter:

Fundamental Integration Formulas:

(i) ∫xndx=x(n+1)(n+1)+C , ∀n≠−1∫xndx=xn+1n+1+C , ∀n≠-1

(ii) ∫x−1dx=∫1xdx=log|x|+C∫x-1dx=∫1xdx=logx+C

(iii) ∫exdx=ex+C∫exdx=ex+C

(iv) ∫axdx=axlog a+C∫axdx=axlog a+C

(v) ∫logx dx=xlogx−x+C∫logx dx=xlogx-x+C

(vi) ∫1x2dx=−1x+C∫1x2dx=-1x+C

(vii) ∫1x√dx=2x−−√+C∫1xdx=2x+C

(viii) ∫sinx dx=−cosx+C∫sinx dx=-cosx+C

(ix) ∫cosx dx=sinx+C∫cosx dx=sinx+C

(x) ∫tanx dx=log|secx|+C∫tanx dx=logsecx+C

(xi) ∫cosecx dx=log|cosecx−cotx|+C∫cosecx dx=logcosecx-cotx+C

(xii) ∫secx dx=log|secx+tanx|+C∫secx dx=logsecx+tanx+C

(xiii) ∫cotx dx=log|sinx|+C∫cotx dx=logsinx+C

(xiv) ∫11−x2√dx=sin−1x+C∫11-x2dx=sin-1x+C

(xv) ∫11+x2dx=tan−1x+C∫11+x2dx=tan-1x+C

(xvi) ∫1xx2−1√dx=sec−1x+C∫1xx2-1dx=sec-1x+C

(xvii) ∫sec2x dx=tanx+C∫sec2x dx=tanx+C

(xviii) ∫cosecx cotx dx=−cosecx+C∫cosecx cotx dx=-cosecx+C

(ix) ∫secxtanx dx=secx+C∫secxtanx dx=secx+C

(xx) ∫cosec2x dx=−cotx+C∫cosec2x dx=-cotx+C

Note: If ∫f(x)dx=F(x)+C∫f(x)dx=F(x)+C, then, ∫f(ax+b)dx=F(ax+b)a+C

NCERT Solutions for Class 12 Maths for All Chapters

Students can refer to these links to the articles for better clarity:

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

FAQs

Q.1. From where can I download the exercise solutions for Integrals for Exercise 7.10 Class 12 Maths?
Ans: Students can download the exercise Solutions for Integrals Exercise 7.10 Class 12 Maths from the official website.

Q2. What are the important topics in Class 12 NCERT Maths Chapter 7 Integrals?
Ans: Important topics in class 12 NCERT Maths Chapter 7 Integrals are as follows:

• 7.1 Introduction to Integral Calculus
• 7.2 Integration as an Inverse Process of Differentiation
• 7.3 Methods of Integration
• 7.4 Integrals of Some Particular Functions
• 7.5 Integration by Partial Fractions
• 7.6 Integration by Parts
• 7.7 Definite Integral
• 7.8 Fundamental Theorem of Calculus
• 7.9 Evolution of Definite Integrals by Substitution
• 7.10 Some Properties of Definite Integrals.

Q.3. How can  NCERT Solutions for Integrals Exercise 7.10 Class 12 Maths help me in class 12 exam preparation?
Ans:  NCERT Solutions for Integrals Exercise 7.10 Class 12 Maths will give a clear picture on the chapter Integrals and its important topics.

Q.4.  Are NCERT textbooks sufficient for board exam preparation?
Ans. The question paper created in the class 12 board exam is based on NCERT textbooks. So it will be enough to get a decent score. But to achieve the best grade, students should also refer to other books from famous publications.

Q.5. Is chapter 7 Integrals maths class 12 difficult?
Ans: Chapter 7 Integrals is an important chapter for class 12. Students must solve Ex.7.10 Class 12 Maths in order to get the best marks and make a few mistakes during the exam. As such the chapter is not very difficult to learn by the students.