NCERT Solutions for Class 12 Maths Chapter 7 Integrals gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Integrals with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 11 exercises (Exercise 7.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 10 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Calculus unit (35 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (3-4 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 7 Integrals NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 7 Integrals
Class 12 Maths Chapter 7 Integrals sits inside the Calculus unit and focuses on indefinite and definite integrals; standard integration formulae; integration by substitution, by parts, and by partial fractions; the fundamental theorem of calculus. The chapter splits into 11 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Integrals Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 7 Integrals Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 7 Integrals: All Exercises
Every exercise of Class 12 Maths Chapter 7 Integrals, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 7.1 | Integrals Exercise 7.1 NCERT Solutions | 22 questions on direct integration using standard formulae. |
| Exercise 7.2 | Integrals Exercise 7.2 NCERT Solutions | 39 questions on integration by substitution. |
| Exercise 7.3 | Integrals Exercise 7.3 NCERT Solutions | 24 questions using trigonometric identities before integrating. |
| Exercise 7.4 | Integrals Exercise 7.4 NCERT Solutions | 25 questions on integrals of the 1/(a-squared minus x-squared) type and their inverse-trig or log forms. |
| Exercise 7.5 | Integrals Exercise 7.5 NCERT Solutions | 23 questions on integration by partial fractions. |
| Exercise 7.6 | Integrals Exercise 7.6 NCERT Solutions | 24 questions on integration by parts using the LIATE rule. |
| Exercise 7.7 | Integrals Exercise 7.7 NCERT Solutions | 11 questions on irrational functions using the completing-the-square technique. |
| Exercise 7.8 | Integrals Exercise 7.8 NCERT Solutions | 22 questions applying the fundamental theorem of calculus to definite integrals. |
| Exercise 7.9 | Integrals Exercise 7.9 NCERT Solutions | 10 questions using definite integral properties like symmetry and the king property. |
| Exercise 7.10 | Integrals Exercise 7.10 NCERT Solutions | 10 questions on definite integrals by substitution, with a limits change. |
| Miscellaneous Exercise | Integrals Miscellaneous Exercise NCERT Solutions | 44 mixed problems combining all ten exercises, used as JEE Main slots. |
Concepts Covered in Class 12 Maths Chapter 7 Integrals
The exercise index above maps each exercise back to these concepts.
- Indefinite Integrals: the +c constant of integration is mandatory; CBSE deducts marks for a missing +c.
- Integration by Substitution: substitute u = g(x), compute du = g-prime(x) dx, then rewrite the integrand in u.
- Integration by Parts: integral of u dv equals uv minus integral of v du; the LIATE rule picks u (Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential).
- Partial Fractions: decompose a rational function into simpler fractions before integrating, handling linear, repeated and quadratic factors.
- Definite Integrals: the fundamental theorem gives integral(a to b) f(x)dx = F(b) - F(a); the king property lets you evaluate without finding F.
Class 12 Maths Chapter 7 Integrals Weightage and Exam Relevance
Chapter 7 Integrals carries approximately 10 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Calculus unit which carries 35 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 10 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 3-4 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 7 Integrals
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Integrals Solutions | Step-by-step answers for every exercise of Integrals (this page). |
| Notes | Open Integrals Notes | Concept-level revision summary for Integrals with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Integrals Formula Sheet | Every formula and standard result from Integrals on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Integrals Handwritten Notes | Notebook-style scanned-look notes for Integrals with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Integrals NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Integrals - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Integrals Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Integrals chapter. |
| Exemplar Book PDF | Open Integrals Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Integrals - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 7 Integrals
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Integrals.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 7 Integrals NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 7 Integrals
- Dropping the +c constant on indefinite integrals; CBSE deducts marks for it.
- Forgetting to change the limits to u after substituting in a definite integral.
- Picking the wrong u in integration by parts instead of using the LIATE rule.
- Using partial fractions without polynomial division first when the numerator's degree is too high.
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 7 Integrals NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 7 Integrals NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 7 Integrals NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 11 exercises in total (Exercise 7.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 7 Integrals?
Ans. Class 12 Maths Chapter 7 Integrals has 11 exercises: Exercise 7.1, Exercise 7.2, Exercise 7.3, Exercise 7.4, Exercise 7.5, Exercise 7.6, Exercise 7.7, Exercise 7.8, Exercise 7.9, Exercise 7.10, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 7 Integrals solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 7 Integrals. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 7 Integrals?
Ans. Chapter 7 Integrals carries approximately 10 marks on the CBSE Class 12 Maths theory paper, sitting inside the Calculus unit which carries 35 marks in total. JEE Main typically asks 3-4 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 7 Integrals is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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