NCERT Solutions Class 12 Mathematics Chapter 7 Integrals

Step-by-Step Textbook Solutions for Class 12 Mathematics Chapter 07 Integrals

Access comprehensive textbook solutions for Chapter 07 Integrals using the official curriculum guides for Class 12 Mathematics. Designed to align with the 2026-27 NCERT standards, these detailed answers help students reinforce core academic concepts.

Download Chapter 07 Integrals Textbook Solutions PDF

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Exercise 7.1

1. Find an anti derivative (or integral) of the following functions by the method of inspection.
sin 2x . 
Answer :

The anti derivative of sin 2x is a function of x whose derivative is sin 2x.
It is known that,

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals

Therefore, the anti derivative of sin2x is -1/2 cos 2x

2. Find an anti derivative (or integral) of the following functions by the method of inspection.
cos 3x . 
Answer :

The anti derivative of cos 3x is a function of x whose derivative is cos 3x.
It is known that,

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-1

3. Find an anti derivative (or integral) of the following functions by the method of inspection.
e2x.
Answer :

The anti derivative of e2is the function of x whose derivative is e2x.
It is known that,

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-2

4. Find an anti derivative (or integral) of the following functions by the method of inspection.
(ax + b)2
Answer :

The anti derivative of (ax + b)2 is the function of x whose derivative is (ax + b)2 . 
It is known that, 

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-3

5. Find an anti derivative (or integral) of the following functions by the method of inspection
sin 2x – 4 e3x
Answer :

The anti derivative of (sin2x - 4e3x) is the function of x whose derivative is (sin 2x - 4e3x). 
It is known that, 

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-4

6. Find the following integrals ∫(4 e3x + 1) dx
Answer :

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-5

7. Find the following integrals ∫[x2 (1 - 1/x2 ) dx 
Answer :

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-6

8. Find the following integrals ∫(ax + bx + c) dx .
Answer :

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-7

9. Find the following integrals ∫(2x2 + ex ) dx .
Answer :

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-8

10. Find the following integrals ∫ (√x - 1/√x)2 dx
Answer :

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-9

11. Find the following integrals ∫[(x3 + 5x2 - 4)/x2 ] dx 
Answer :

""NCERT-Solutions-Class-12-Mathematics-Chapter-7-Integrals-10

 

 

 

Free NCERT Textbook Explanations: Class 12 Mathematics Chapter 07 Integrals

Official NCERT Solutions for Chapter 07 Integrals

Review comprehensive exercise answers for Class 12 Mathematics Chapter 07 Integrals. Fully updated to match current NCERT syllabus guidelines, these textbook solutions help students verify their work and maintain accurate study notes.

Step-by-Step Explanations for Chapter 07 Integrals

Clear, methodical explanations accompany every challenging problem within the Class 12 Mathematics text. Engaging with these detailed answers lays a solid foundation for advanced learning and improves foundational clarity for upcoming assessments.

Next Steps in Your Mathematics Revision

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FAQs

Where can I find the latest NCERT Solutions Class 12 Mathematics Chapter 7 Integrals for the 2026-27 session?

The complete and updated NCERT Solutions Class 12 Mathematics Chapter 7 Integrals is available for free on StudiesToday.com. These solutions for Class 12 Mathematics are as per latest NCERT curriculum.

Are the Mathematics NCERT solutions for Class 12 updated for the new 50% competency-based exam pattern?

Yes, our experts have revised the NCERT Solutions Class 12 Mathematics Chapter 7 Integrals as per 2026 exam pattern. All textbook exercises have been solved and have added explanation about how the Mathematics concepts are applied in case-study and assertion-reasoning questions.

How do these Class 12 NCERT solutions help in scoring 90% plus marks?

Toppers recommend using NCERT language because NCERT marking schemes are strictly based on textbook definitions. Our NCERT Solutions Class 12 Mathematics Chapter 7 Integrals will help students to get full marks in the theory paper.

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