NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Exercise 7.1

Quick Navigation – Jump to Question

Chapter 7 – Integrals Exercise 7.1

1.

Q1 basic integration problem from NCERT Class 12 Integrals Exercise 7.1
Q1 NCERT solution with standard integration steps

2.

Q2 standard integral function with constant multiplier
Q2 simplified integration result using constants

3.

Q3 integral question involving polynomial terms
Q3 polynomial term integration shown step-wise

4.

 Q4 Class 12 question on integrating algebraic expressions
Q4 complete solution for algebraic integration

5.

Q5 integration using standard formulas from Exercise 7.1
Q5 integration using NCERT standard formula list

6.

Q6 NCERT integration question with square root expression
Q6 answer image showing root-based integral simplification

7.

 Q7 integral question involving variable substitution
Q7 integral solved using substitution technique

8.

Q8 integration of a rational function
Q8 rational function integration shown with steps

9.

Q9 Class 12 integration using u-substitution method
Q9 step-by-step solution using substitution method

10.

Q10 NCERT integration problem with multiple terms
Q10 multi-term integral simplified to final answer

11.

Q11 question on definite integral evaluation
Q11 definite integral with limits applied and simplified

12.

Class-12 Integrals Exercise-7.1 Question 12 - integral of trigonometric function-NCERT
Q12 trigonometric function integrated and simplified

13.

Class-12 Integrals Exercise-7.1 Question 13-integral question with sine and cosine functions- NCERT
Class-12 Integrals Exercise-7.1 Question 13 sine and cosine integration solution- NCERT Answer

14.

Class-12 Integrals Ex-7.1 Question 14 - problem on integration of exponentials - NCERT
Class-12 Integrals Exercise-7.1 Question 14 integration involving exponentials with constant base
- NCERT Answer

15.

Class-12 Integrals Exercise-7.1 Question 15 -exponential function integration- NCERT
Class-12 Integrals Exercise-7.1 Question 15 answer for exponential integration- NCERT Answer

16.

Class-12 Integrals Exercise-7.1 Question 16 -integration of logarithmic expressions- NCERT
Class-12 Integrals Exercise-7.1 Question 16 log expression integration and simplification
- NCERT Answer

17.

Class-12 Integrals Exercise-7.1 Question 17 -integral with natural logarithm and constants- NCERT
Class-12 Integrals Exercise-7.1 Question 17 solution involving natural logarithm integral- NCERT Answer

18.

Class-12 Integrals Exercise-7.1 Question 18 -integration involving mixed algebraic functions- NCERT
Class-12 Integrals Exercise-7.1 Question 18 mixed function integration worked through in steps- NCERT Answer

19.

Class-12 Integrals Exercise-7.1 Question 19 -integration question with fractional expression- NCERT
Class-12 Integrals Exercise-7.1 Question 19 fractional expression simplified via integration- NCERT Answer

20.

Class-12 Integrals Exercise-7.1 Question 20-involving integration by parts- NCERT
Class-12 Integrals Exercise-7.1 Question 20 integration by parts shown step-by-step- NCERT Answer

21.

Class-12 Integrals Exercise-7.1 Question 21- advanced integration of algebraic fractions-NCERT
Class-12 Integrals Exercise-7.1 Question 21 solution for algebraic fractions integration- NCERT Answer

22.

Class-12 Integrals Exercise-7.1 Question 22-final integration problem combining standard identities- NCERT
Class-12 Integrals Exercise-7.1 Question 22 final integration using identity-based approach- NCERT Answer

Download Exercise 7.1 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 7.2View 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 7.1 Overview

Exercise 7.1 is the ideal starting point if you are just beginning with integration. It presents the idea of integration as the reverse of differentiation, therefore enabling you to “undo” what derivatives accomplish. This exercise provides a strong head start before you go into more difficult techniques later in the chapter and is all about learning standard integration formulas.

Mostly working on problems where you directly apply these concepts, Integrals Class 12 NCERT Solutions Ex 7.1 These can call for logarithms, exponentials, trigonometric functions, and algebraic expressions. The good news is that These questions become really easy as you become acquainted to the patterns—and even enjoyable to answer!

This practice is especially important for getting you ready for entrance tests like JEE and CUET as well as for your board tests using the revised 2025 NCERT Class 12 Maths syllabus. One of those syllabus components that may seem basic at first yet sets the tone for the whole chapter.

Spending time on Chapter 7 Class 12 NCERT Solutions Exercise 7.1 can help you get confident and begin to see how integration works. This is a fantastic chance to improve your fundamentals and become at ease with the tools you will be using going forward—and past.

FAQs – Integrals Class 12 Exercise 7.1 NCERT

Do I need to memorize all the integration formulas?

Yes, but don’t worry—it gets easier with practice. Start by understanding each formula, then solve the problems in Integrals Class 12 NCERT Solutions Exercise 7.1 to reinforce them.

How is this exercise useful in real exams?

This part often shows up in both boards and competitive exams. It may seem easy, but scoring full marks here is a big win if you’ve practiced well.

What if I’m confused about which formula to use?

That’s totally normal at first! Try to identify the type of function given—like trigonometric or exponential—and match it with the standard form. Keep a formula chart nearby as you practice.

Where can I find step-by-step help?

You can head over to Cogniks.com for detailed solutions to Integrals Class 12 NCERT Solutions Exercise 7.1. We explain each step in a student-friendly way so it’s easy to follow and learn.

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