NCERT Solutions for Class 12 Maths Chapter 7 – Integrals
NCERT Solutions for Class 12 Maths Chapter 7 – Integrals at Myclass24 are crafted to help students master one of the most extensive chapters in the CBSE Class 12 syllabus. Integration is essentially the reverse of differentiation, but it demands an entirely different set of skills and techniques. Our solutions walk students through every exercise with clear steps, well-labelled methods, and a focus on building conceptual clarity alongside problem-solving speed.
Summary of Chapter 7 Integrals
Integrals-Indefinite Integrals: Introduction basic concepts, Standard result, Algebra of Integration, Methods of integrations, Integration by substitution Integration using trigonometric identities. Integration of some particular functions. Partial fraction, Integration by parts, Special Integral of Type
Find the PDF of NCERT Solutions for Class 12 Maths Chapter 7
The PDF of NCERT Solutions for Class 12 Maths Chapter 7 – Integrals is available on Myclass24. Students can access all exercise-wise solutions in a clean, printable format. The PDF is structured to match the textbook order, making it easy to follow along while studying. Download and keep it handy during your revision sessions for quick reference before tests and board exams.
Detail | Information |
Chapter | Chapter 7 – Integrals |
Class | Class 12 Maths |
Board | CBSE (NCERT) |
Total Exercises | 11 Exercises + Miscellaneous |
Topics Covered | Indefinite Integrals, Methods of Integration, Definite Integrals, Fundamental Theorem of Calculus |
Difficulty Level | High |
Content By | Myclass24 |
About Chapter 7 – Integrals
Chapter 7 is one of the longest chapters in the entire Class 12 Maths textbook, and for good reason — integration has multiple methods, each suited to a different type of function. The chapter opens with the concept of indefinite integration as the anti-derivative, establishing the standard forms that students must remember, such as the integrals of trigonometric functions, exponential functions, and power functions.
The methods of integration form the heart of this chapter. Substitution is introduced early, in exercises like 7.2, where students learn to simplify a complex integral by substituting a part of the expression with a new variable. This method becomes second nature with practice and is used extensively throughout the chapter.
Integration by parts, covered in Exercise 7.6, follows the formula ∫u dv = uv − ∫v du. Choosing which function to treat as u — using the ILATE rule — is a decision that students need to make correctly, and our solutions at Myclass24 explain the reasoning behind each choice rather than just stating the answer.
Partial fractions, covered in Exercise 7.5, are used when the integrand is a rational function. Decomposing expressions like 1/(x²−1) into simpler fractions before integrating requires careful algebraic manipulation. The solutions here show every factorisation step clearly.
Definite integrals, beginning from Exercise 7.8, introduce limits of integration and connect to the Fundamental Theorem of Calculus. Students evaluate integrals between two specific values, and the chapter includes elegant properties of definite integrals — such as the property where the integral from a to b equals the integral from a to b of f(a+b−x)dx — which simplify seemingly difficult problems to very clean ones.
The Miscellaneous Exercise tests all methods together and is considered quite challenging. At Myclass24, our solutions for these problems include alternative approaches wherever applicable so students see more than one way to reach the result.
Why Study Chapter 7 from Myclass24?
At Myclass24, every solution for Chapter 7 is crafted keeping the CBSE exam pattern in mind. The explanations are written in plain language, the steps are numbered clearly, and important formulas are highlighted where needed. Students preparing for board exams, or anyone who wants to genuinely understand Integrals, will find Myclass24 solutions both reliable and thorough.
NCERT Solutions for Class 12 Maths Chapter 7 – Integrals FAQs
Integration is the mathematical process of finding the antiderivative of a function. It is often described as the reverse operation of differentiation because it helps recover a function from its derivative. In Chapter 7, students learn various methods of integration and their applications in solving mathematical problems. NCERT exercises introduce the concept gradually, starting with basic formulas and progressing to more complex techniques. Understanding the relationship between differentiation and integration is essential because it forms the foundation of calculus. A strong grasp of this concept helps students solve integration problems accurately and prepares them for advanced mathematical topics.
Standard integration formulas form the backbone of this chapter and are used repeatedly throughout NCERT exercises. These formulas include the integrals of algebraic, trigonometric, exponential, and logarithmic functions. Students should focus on understanding the formulas rather than memorising them mechanically. Many questions can be solved quickly once the appropriate formula is identified. NCERT problems often require the direct application of standard results as well as their use in more complicated expressions. Regular revision of important formulas improves confidence and calculation speed. A strong command of these formulas makes solving integration questions much easier during examinations.
The method of substitution is one of the most widely used techniques for solving integrals. It involves replacing a complicated expression with a simpler variable to transform the integral into an easier form. Students first identify a suitable substitution, differentiate it, and then rewrite the integral accordingly. NCERT exercises contain many examples where substitution helps simplify algebraic and trigonometric expressions. Choosing the correct substitution is often the key to solving a problem efficiently. With regular practice, students learn to recognise patterns and apply this technique confidently. Mastering substitution significantly improves problem-solving ability in integration-based questions.
Integration by parts is a technique used when an integral involves the product of two functions. The method is based on a standard formula that transforms the original integral into a simpler one. Students must carefully choose which function to differentiate and which to integrate. NCERT exercises provide various examples involving algebraic, logarithmic, exponential, and trigonometric functions. A proper choice of functions often determines the ease of the solution. Understanding the logic behind this method helps students apply it effectively rather than relying on trial and error. Consistent practice strengthens confidence in handling complex integration problems.
Many students make errors by selecting incorrect integration formulas or overlooking constants during calculations. Another common mistake is applying substitution or integration by parts without properly transforming the entire expression. Algebraic simplification errors can also lead to incorrect answers. Some students forget to add the constant of integration after completing the solution. NCERT exercises encourage careful step-by-step problem-solving to minimise these mistakes. Regular practice and revision of formulas help students identify the most suitable method for each question. Developing accuracy and patience while solving integrals is essential for achieving strong performance in board examinations and competitive tests.