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NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Exercise 7.4

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Chapter 7 – Integrals Exercise 7.4

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Q1 NCERT Class 12 question involving integration of rational function

Q1 integration steps using partial fraction decomposition

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Q2 integration using partial fractions and algebraic terms

Q2 rational integrand broken into simpler parts

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Q3 Class 12 NCERT problem on simplifying rational integrand

Q3 step-by-step resolution of rational expression

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Q4 question on integration using factorization of polynomial

Q4 integration via partial fraction and simplification

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Q6 Class 12 integration involving linear and quadratic terms

integrand split and each part integrated separately

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Class-12 Integrals Exercise-7.4 Question 6- NCERT

Q6 breakdown of complex rational function

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Q7 rational function integration by splitting termsc

Q7 integration steps involving polynomial and fraction

Q7 answer showing simplified integrated value

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Q8 polynomial function in denominator simplified for integration

Q8 NCERT integration with step-by-step simplification

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Q9 question involving algebraic manipulation before integration

Q9 Class 12 question solved using algebraic techniques

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Q10 integration using substitution and partial fractions

Q10 integration using substitution and decomposition

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Q11 Class 12 NCERT rational integration with multiple terms

Q11 stepwise resolution of integrand using parts

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Q12 integrand involves partial fractions with repeated roots

Q12 rational integrand solved via partial fractions

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Class-12 Integrals Exercise-7.4 Question 13 - requiring decomposition of rational function- NCERT

Class-12 Integrals Exercise-7.4 Question 13 algebraic expression simplified for integration- NCERT Answer

Class-12 Integrals Exercise-7.4 Question 13 detailed answer from Exercise 7.4- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 14 integrand decomposed into partial fractions- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 15 -integration involving improper rational function- NCERT

Class-12 Integrals Exercise-7.4 Question 15 polynomial division and integration applied- NCERT Answer

Class-12 Integrals Exercise-7.4 Question 15 integral final result- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 16 -polynomial division followed by integration- NCERT

Class-12 Integrals Exercise-7.4 Question 16 simplification of rational form- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 17-integration using decomposition and simplification
- NCERT

Class-12 Integrals Exercise-7.4 Question 17 integrand rearranged and integrated step-by-step- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 18 -integrand contains rational function needing rearrangement- NCERT

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Class-12 Integrals Exercise-7.4 Question 19 -involves algebraic fraction suitable for parts- NCERT

Q19 final simplified result of integration

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Class-12 Integrals Exercise-7.4 Question 20-problem on resolving into partial fractions- NCERT

Class-12 Integrals Exercise-7.4 Question 20 rational expression broken down into parts- NCERT Answer

Class-12 Integrals Exercise-7.4 Question 20 complete answer with constant- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 21-rational expression integration involving substitution- NCERT

Class-12 Integrals Exercise-7.4 Question 21 integration steps using substitution technique- NCERT Answer

Class-12 Integrals Exercise-7.4 Question 21 simplified and complete integration result- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 22-integration requiring simplification and rearrangement -NCERT

Class-12 Integrals Exercise-7.4 Question 22 step-by-step integration of complex rational term- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 23-question with polynomial numerator and denominator- NCERT

Class-12 Integrals Exercise-7.4 Question 23 polynomial term integration via long division- NCERT Answer

Class-12 Integrals Exercise-7.4 Question 23 full final answer with all components- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 24-integrand with quadratic denominator- NCERT

Class-12 Integrals Exercise-7.4 Question 24 integration of rational function involving quadratic- NCERT Answer

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Class-12 Integrals Exercise-7.4 Question 25-integration question combining multiple algebraic steps -NCERT

Download Exercise 7.4 NCERT Solutions PDF

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Download Chapter 7 – Integrals NCERT Solutions PDF

Class 12 Maths Chapter 7 – Integrals: All Exercises

Exercise	Link
Exercise 7.1	View Solutions
Exercise 7.2	View Solutions
Exercise 7.3	View Solutions
Exercise 7.5	View Solutions
Exercise 7.6	View Solutions
Exercise 7.7	View Solutions
Exercise 7.8	View Solutions
Exercise 7.9	View Solutions
Exercise 7.10	View Solutions
Miscellaneous Exercise	View Solutions

Class 12 Integrals- Exercise 7.4 Overview

Exercise 7.4 marks the beginning of things getting somewhat more visually appealing and enjoyable! This chapter section will assist you in solving integrals utilizing trigonometric identities. Exercise 7.4 of Chapter 7 Integrals takes a rather different route—it’s about smart simplification utilizing formulas you’ve already learned in trigonometry, while earlier exercises concentrated on substitution and parts.

Often dealing with expressions like sin²x or cos²x, you will find great benefit from identities like sin²x = (1 – cos 2x/2). This practice truly sharpens your formula-handing abilities and is a superb blend of algebra, trigonometry, and integration.

The 2025 NCERT Class 12 Maths syllabus claims that this idea is now even more important given its practical uses in fields such signal processing, physics, and calculus-based modelling. Practicing these kinds of questions can help you identify more quickly when and how to use identities to break down tough-looking integrals.

Using merely your trigonometry foundations, Integrals Class 12 NCERT Solutions Ex 7.4 will help you develop the confidence to simplify difficult equations. Turning a difficult integral into something tidy and manageable will make you very happy once you get the hang of it.

FAQs – Integrals Class 12 Exercise 7.4 NCERT

Exercise 7.4 makes mostly use which technique?

This assignment mostly emphasizes on simplifying integrals before calculating them using trigonometric identities.

How do I determine which identity to use?

That relies on the expression. Use the ordinary reduction identities for powers such as sin²x or cos²x. With products, search for formulations that translate them into sums or differences.

Does one need learning identities to solve Exercise 7.4?

Undoubtedly! Just a few fundamental ones—like those for sin(x)cos(x), sin²x, cos²x—will cover most issues here; you do not have to learn many.

Are these questions included in board examinations?

Surely! Common on both CBSE boards and competitive tests like JEE, trigonometric integrals are seen in both, hence Integrals Class 12 NCERT Solutions Exercise 7.4 is most surely worth your effort.

Where might I find condensed answers for Exercise 7.4?

Cogniks.com provides all of the Integrals Class 12 NCERT Solutions Exercise 7.4 questions together with detailed step-by-step direction meant for improved understanding.