NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Exercise 7.8

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Chapter 7 – Integrals Exercise 7.8

1.

Q1 Class 12 integration question involving definite limits and identity
Q1 step-by-step integration using identity and substitution

2.

Q2 definite integral using properties of even and odd functions
Q2 definite integral setup using function property

3.

Q3 NCERT integral requiring substitution and symmetry
Q3 substitution used to transform the integral
Q3 final integration answer after simplification

4.

Q4 question on evaluating integral using standard trigonometric identities
Q4 integral solved using standard trig identities

5.

Q5 Class 12 question with rational expression and transformation
Q5 setup using rational function transformation

6.

Q6 integral involving root and polynomial combination under limits
Q6 square root expression integrated step-by-step

7.

Q7 algebraic integral requiring limits and substitution method
Q7 substitution and integration under limits

8.

Q8 Class 12 integration question using identity and reduction
Q8 identity-based simplification of definite integral

9.

Q9 definite integral solved using trigonometric simplification
Q9 trigonometric simplification method shown

10.

Q10 NCERT question involving logarithmic function and definite range
Q10 logarithmic function handled under definite range

11.

Q11 integral involving trigonometric function and product simplification
Q11 product of trigonometric functions solved

12.

Class-12 Integrals Exercise-7.8 Question 12-question using exponential functions and substitution- NCERT
Class-12 Integrals Exercise-7.8 Question 12 exponential substitution used to simplify- NCERT Answer

13.

Class-12 Integrals Exercise-7.8 Question 13 -integral with squared trigonometric function under limits- NCERT
Class-12 Integrals Exercise-7.8 Question 13 square trigonometric expression solved- NCERT Answer

14.

Class-12 Integrals Exercise-7.8 Question 14 -definite integral based on odd function symmetry-NCERT
Class-12 Integrals Exercise-7.8 Question 14 use of symmetry to simplify definite integral- NCERT Answer

15.

Class-12 Integrals Exercise-7.8 Question 15-integration involving algebraic expression with transformation-NCERT
Class-12 Integrals Exercise-7.8 Question 15 polynomial transformation and integration setup- NCERT Answer

16.

Class-12 Integrals Exercise-7.8 Question 16 - problem using substitution and limit change-NCERT
Class-12 Integrals Exercise-7.8 Question 16 substitution and integration over changed limits- NCERT Answer
Class-12 Integrals Exercise-7.8 Question 16 answer evaluated under definite bounds- NCERT Answer

17.

Class-12 Integrals Exercise-7.8 Question 17 -integration requiring square identity simplification- NCERT
Class-12 Integrals Exercise-7.8 Question 17 identity applied for simplification of square- NCERT Answer

18.

Class-12 Integrals Exercise-7.8 Question 18 -integration problem with rational function in denominator-NCERT
Class-12 Integrals Exercise-7.8 Question 18 integration setup using rational expression- NCERT Answer

19.

Class-12 Integrals Exercise-7.8 Question 19 - integration using change of limits and simplification-NCERT
Class-12 Integrals Exercise-7.8 Question 19 function simplified using limit transformation- NCERT Answer
Class-12 Integrals Exercise-7.8 Question 19 final result of definite integral- NCERT Answer

20.

Class-12 Integrals Exercise-7.8 Question 20-definite integral combining trigonometric identities- NCERT
Class-12 Integrals Exercise-7.8 Question 20 solution using trigonometric identity properties
- NCERT Answer

21.

Class-12 Integrals Exercise-7.8 Question 21-integration of rational and logarithmic functions- NCERT
Class-12 Integrals Exercise-7.8 Question 21 integration of logarithmic and rational function- NCERT Answer

22.

Class-12 Integrals Exercise-7.8 Question 22-definite integral requiring identity-based simplification- NCERT
Class-12 Integrals Exercise-7.8 Question 22 algebraic identity applied in definite integral- NCERT Answer

Download Exercise 7.8 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 7.2View Solutions
Exercise 7.3View Solutions
Exercise 7.4View Solutions
Exercise 7.5View Solutions
Exercise 7.6View Solutions
Exercise 7.7View Solutions
Exercise 7.9View Solutions
Exercise 7.10View Solutions
Miscellaneous ExerciseView Solutions

Class 12 Integrals- Exercise 7.8 Overview

The last stretch of the integrals chapter, Exercise 7.8 is also a vital overview of all you have thus far learned. It examines your ability to use all important integration methods—including substitution, integration by parts, and using conventional formulas—in a range of ways. Consider this exercise as a challenge round training you for the kinds of questions in board tests or competitive exams.

Integrals Class 12 NCERT Solutions Exercise 7.8 is beautiful in how it helps you to improve your decision-making about which approach to use for every problem. Should you consider substitution? Alternatively would it be advisable to apply partial fractions? Perhaps by parts’ integration. Here your conceptual clarity truly shines.

This exercise keeps emphasising application-based, multi-step integration challenges in keeping with the revised 2025 NCERT syllabus. It’s meant to increase your confidence as much as your ability to solve problems. With experience, you will learn how to approach integrals from several sides and reduce even the most complicated-looking statements.

Completing Integrals Class 12 NCERT Solutions Exercise 7.8 will help you to firmly grasp all the integral techniques, therefore strengthening your basis for next math subjects and practical uses

FAQs – Integrals Class 12 Exercise 7.8 NCERT

Does solving this exercise depend on remembering all formulas?

Indeed, one needs a solid memory of basic integration techniques. More critical though, is knowing when to use them.

Which of substitution, parts, or standard approach should I apply?

It is something one gains experience with. search for trends:
Complex brackets? Try substitute.
Two-fold function product Try using parts to integrate.
Rational statements Use partial fractions

Does the board exam include questions from Exercise 7.8?

Certainly! Because of their thorough steps, these are widely asked problems—typically 4- or 6-mark questions.

I make mistakes in long calculations. Any tips?

Break down the problem into smaller steps. Write correctly, and double-check your derivative or substitution before integration.

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