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.
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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,
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,
3. Find an anti derivative (or integral) of the following functions by the method of inspection.
e2x.
Answer :
The anti derivative of e2x is the function of x whose derivative is e2x.
It is known that,
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,
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,
6. Find the following integrals ∫(4 e3x + 1) dx
Answer :
7. Find the following integrals ∫[x2 (1 - 1/x2 ) dx
Answer :
8. Find the following integrals ∫(ax + bx + c) dx .
Answer :
9. Find the following integrals ∫(2x2 + ex ) dx .
Answer :
10. Find the following integrals ∫ (√x - 1/√x)2 dx
Answer :
11. Find the following integrals ∫[(x3 + 5x2 - 4)/x2 ] dx
Answer :
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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.
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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.
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.
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