NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Exercise 7.2

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Chapter 7 – Integrals Exercise 7.2

1.

Q1 Class 12 integration problem using substitution
Q1 solution showing substitution and final integrated result

2.

Q2 NCERT integral involving root expressions
Q2 answer for root-based integration simplified

3.

 Q3 standard function integration using algebraic simplification
Q3 Class 12 NCERT solution with simplification steps

4.

Q4 basic integral using identity formula
Q4 integration using identity and direct formula

5.

Q5 integration question with rational expression
Q5 rational function solved with integration formula

6.

Q6 exercise 7.2 question with square terms
Q6 answer image with algebraic term simplification

7.

Q7 NCERT question involving algebraic fraction
Q7 rational expression integrated using known identities

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Q8 integration requiring use of trigonometric substitutio
Q8 substitution and rearrangement used in final solution

9.

Q9 rational function integration from Class 12 NCER
Q9 step-by-step simplification for Class 12 integral

10.

Q10 Class 12 question on algebraic simplification before integration
Q10 NCERT solution applying u-substitution

11.

 Q11 integral with constant and variable combination
Q11 algebraic simplification followed by integration

12.

Q12 integral solved using basic formula application

13.

Q13 advanced algebraic integration expression
Q13 answer using rational function integration

14.

Q14 Class 12 integral of polynomial divided by binomial
Q14 simplified polynomial with constant multiplier

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Q15 integral involving perfect square simplification
Q15 square terms simplified and integrated

16.

Q16 NCERT question with trigonometric format inside integral
Q16 trigonometric expression solved with substitution

17.

Q17 standard rational expression requiring simplification
Q17 rational term integrated using standard method

18.

Q18 expression with partial fractions for integration
Q18 NCERT solution with partial fractions used

19.

Q19 Class 12 problem requiring identity substitution
Q19 integration shown with identity and formula

20.

Q20 NCERT exercise with multi-term rational expression
Q20 multi-step integration with rearrangement.

21.

Class-12 Integrals Exercise-7.2 Question 21-integration question requiring completing the square
- NCERT
Class-12 Integrals Exercise-7.2 Question 21 completing the square and integration result- NCERT Answer

22.

Class-12 Integrals Exercise-7.2 Question 22-trigonometric form integration using identities- NCERT
Class-12 Integrals Exercise-7.2 Question 22 trigonometric integral simplified to answer- NCERT Answer

23.

Class-12 Integrals Exercise-7.2 Question 23-rational function with cube terms inside integrand-NCERT
Class-12 Integrals Exercise-7.2 Question 23  answer with cube term integration steps- NCERT Answer

24.

Class-12 Integrals Exercise-7.2 Question 24-question combining polynomials and trigonometric functions-NCERT
Class-12 Integrals Exercise-7.2 Question 24 mixed expression integrated logically- NCERT Answer

25.

Class-12 Integrals Exercise-7.2 Question 25 -complex algebraic expression requiring simplification- NCERT
Class-12 Integrals Exercise-7.2 Question 25 detailed simplification and integration steps- NCERT Answer

26.

Class-12 Integrals Exercise-7.2 Question 26-integral of expression involving square root and variable
- NCERT
Class-12 Integrals Exercise-7.2 Question 26 root expression integrated via substitution - NCERT Answer

27.

Class-12 Integrals Exercise-7.2 Question 27-integration question using standard identity-NCERT
Class-12 Integrals Exercise-7.2 Question 27 integration using trigonometric substitution- NCERT Answer

28.

Class-12 Integrals Exercise-7.2 Question 28-integral of algebraic expression with binomial expansion NCERT
Class-12 Integrals Exercise-7.2 Question 28 binomial term integrated with expansion- NCERT Answer

29.

Class-12 Integrals Exercise-7.2 Question 29 -integration question using u-substitution- NCERT
Class-12 Integrals Exercise-7.2 Question 29 solution using u-substitution method- NCERT Answer

30.

Class-12 Integrals Exercise-7.2 Question 30 -standard form requiring rearrangement before integrating- NCERT
Class-12 Integrals Exercise-7.2 Question 30 formula-based solution with clear steps- NCERT Answer

31.

Class-12 Integrals Exercise-7.2 Question 31-algebraic identity-based integration expression-NCERT
Class-12 Integrals Exercise-7.2 Question 31 algebraic identity used for simplification- NCERT Answer

32.

Class-12 Integrals Exercise-7.2 Question 32-rational function simplified with long division method-NCERT
Class-12 Integrals Exercise-7.2 Question 32 long division followed by integration steps- NCERT Answer

33.

Class-12 Integrals Exercise-7.2 Question 33-integration involving sum and difference of functions-NCERT
Class-12 Integrals Exercise-7.2 Question 33 integral using term-wise integration- NCERT Answer

34.

Class-12 Integrals Exercise-7.2 Question 34-trigonometric identity application in integration-NCERT
Class-12 Integrals Exercise-7.2 Question 34 trigonometric identity-based integration- NCERT Answer

35.

Class-12 Integrals Exercise-7.2 Question 35- polynomial integral simplified with linear combination
- NCERT
Class-12 Integrals Exercise-7.2 Question 35 linear combination simplified and integrated- NCERT Answer

36.

Class-12 Integrals Exercise-7.2 Question 36-rational expression requiring substitution technique- NCERT
Class-12 Integrals Exercise-7.2 Question 36 rational expression solved through substitution- NCERT Answer

37.

Class-12 Integrals Exercise-7.2 Question 37-requiring advanced simplification before integration-NCERT
Class-12 Integrals Exercise-7.2 Question 37 solution with multi-step integration- NCERT Answer

38.

Class-12 Integrals Exercise-7.2 Question 38-integration of polynomial with square root expression-NCERT
Class-12 Integrals Exercise-7.2 Question 38 root and variable integrated through substitution- NCERT Answer

39.

Class-12 Integrals Exercise-7.2 Question 39-complex Class 12 integral combining algebra and trig
-NCERT
Class-12 Integrals Exercise-7.2 Question 39 algebraic and trigonometric expression integrated together- NCERT Answer

Download Exercise 7.2 NCERT Solutions PDF

You can download the PDF from the link below for offline study

Class 12 Maths Chapter 7 – Integrals: All Exercises

ExerciseLink
Exercise 7.1View Solutions
Exercise 7.3View Solutions
Exercise 7.4View Solutions
Exercise 7.5View Solutions
Exercise 7.6View Solutions
Exercise 7.7View Solutions
Exercise 7.8View Solutions
Exercise 7.9View Solutions
Exercise 7.10View Solutions
Miscellaneous ExerciseView Solutions

Class 12 Integrals- Exercise 7.2 Overview

Exercise 7.1’s conventional formulas are now second nature to you; Exercise 7.2 advances matters by including the replacement technique. Consider this method as a clever shortcut: by varying the variable, you can simplify a tough-looking integral.

In Integrals Class 12 NCERT Solutions Exercise 7.2 you will investigate how substitution simplifies the integration of complicated functions, particularly those that do not directly match the traditional formulas. This method comes up often on boards and competitive tests like JEE and CUET and is quite helpful in solving practical difficulties.

The best thing about this activity is it helps you to see issues more imaginatively. It teaches your brain to see trends and consider how varying factors might provide answers. These fundamental ideas are highly emphasized in the 2025 NCERT Class 12 Maths syllabus, hence learning substitution now will help future subjects like differential equations and definite integrals considerably easier.

By working with Integrals Class 12 NCERT Solutions Exercise 7.2, you not only deepen your knowledge but also get confidence in handling challenging tasks. Not only in tests but also in disciplines including physics, economics, and engineering too, this is one of those abilities you will discover valuable on repeated occasions.

FAQs – Integrals Class 12 Exercise 7.2 NCERT

In integrating, what is the substitution technique?

This is a method whereby the integral is simplified by changing the variable. For instance, simplifying a difficult equation into a basic one compliant with conventional formulas.

When would I be using substitution?

Look for a function and its derivative within the expression if the integral does not fit a typical formula. Usually, this is a good indication to consider substitution. 

Is Exercise 7.2 more challenging than Exercise 7.1?

It’s different, not more difficult. Exercise 7.1 was on using known formulas; Exercise 7.2 focuses more on recognizing trends and selecting the appropriate substitution.

Are all kinds of integrals able to employ substitution?

Not always. It is most effective when the structure of the function permits simplification via variable modification. With practice, you will improve in spotting these.

Where can I get methodically detailed answers?

On Cogniks.com, Integrals Class 12 NCERT Solutions Exercise 7.2 allows you to review every question in an understandable, simple, easily followed manner.

Class 12 Maths Chapters

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

Important Questions for Class 12