Rbse Solutions Class 12 Maths Chapter 7 Miscellaneous | Chapter 7: Integrals

17/03/202616/03/2026 by By Subject Experts

Get complete solutions for the NCERT Class 12 Maths Miscellaneous Exercise on Integrals (Chapter 7). This review covers advanced problems using all techniques: Substitution, Integration by Parts, Partial Fractions, Trigonometric Identities, and Properties of Definite Integrals ($\int_a^b f(x) dx$). Essential practice for board exams and competitive tests. This exercise covers various integration techniques including Substitution, … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.10 | Properties of Definite Integrals

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.10. Learn to evaluate complex definite integrals efficiently by applying key properties like P3 ($\int_0^a f(x) dx = \int_0^a f(a – x) dx$) and P6 ($\int_{-a}^a f(x) dx$). Covers integrals of trigonometric, logarithmic, and modulus functions, focusing on parity (odd/even functions) and simplification techniques. This exercise evaluates … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.9 | Definite Integrals by Substitution

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.9, focusing on solving definite integrals using the substitution method. Learn the crucial step of changing the limits of integration and apply the technique to various functions, including trigonometric, inverse trigonometric, and rational functions. Includes application of the Leibniz rule for differentiating an integral. This exercise focuses … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.7 | Integration using Three Special Formulas

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.7. Master the integration of functions involving the square root of a quadratic expression ($\mathbf{\sqrt{x^2 \pm a^2}}$ and $\mathbf{\sqrt{a^2 – x^2}}$). Covers the essential technique of completing the square to transform expressions before applying the three standard formulas. This exercise requires the use of the three special … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.8 | Definite Integrals

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.8. Learn to evaluate definite integrals using the Fundamental Theorem of Calculus, $\int_a^b f(x) dx = F(b) – F(a)$. Covers various types of definite integrals, including trigonometric, inverse trigonometric, exponential, and fractional functions, along with techniques like substitution and algebraic manipulation. This exercise requires evaluating definite integrals … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.6 | Integration by Parts

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 7.6 on Integrals. Master the Integration by Parts (ILATE) rule for product functions. Covers various types, including inverse/logarithmic functions ($\int x \tan^{-1} x dx$), powers ($\int x^2 e^x dx$), and integrals of the form $\int e^x [f(x) + f'(x)] dx$. This exercise focuses on the integration technique … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.5 | Integration using Partial Fractions Solutions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.5. Master the technique of Partial Fraction Decomposition to integrate rational functions with linear, repeated, and irreducible quadratic factors. Includes advanced substitution problems like $\int \frac{1}{x(x^n + 1)} dx$ and $\int \frac{1}{e^x – 1} dx$. This exercise involves integrating rational functions by decomposing them into simpler fractions … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.4 | Integration using Special Formulas

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.4 on Integrals. Learn to apply the six standard formulas for integration involving $\mathbf{x^2 \pm a^2}$ and $\mathbf{\sqrt{x^2 \pm a^2}}$. Covers the crucial technique of completing the square and integrating types like $\int \frac{px+q}{\text{quadratic}} dx$. This exercise focuses on using the six standard integration formulas involving $\mathbf{x^2 … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.3 | Integration using Trigonometric Identities Solutions

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 7.3 on Integrals. Learn to transform complex trigonometric integrals using Product-to-Sum, Power Reduction ($\sin^2 x$, $\cos^4 x$), and other key identities. Covers types like $\int \sin A \cos B dx$ and $\int \frac{\cos x – \sin x}{1 + \sin 2x} dx$. This exercise requires transforming the integrand … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.1 | Integrals Solutions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.1 on Integrals. Learn to find the anti-derivative of functions like $\sin 2x$, $\cos 3x$, and $(ax+b)^2$ using the method of inspection and applying fundamental integration formulas for polynomials and exponential functions. This exercise introduces the basic concept of integration (finding the anti-derivative) using fundamental formulas and … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.2 | Integration by Substitution Solutions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.2 on Integrals. Master the method of substitution (u-Substitution) to solve complex integrals involving algebraic, trigonometric, and exponential functions, including types like $\int f(g(x))g'(x) dx$ and special trigonometric forms like $\int \frac{1}{1 \pm \tan x} dx$. This exercise focuses entirely on integration by the method of substitution … Read more