NCERT Solutions for Class 12 Mathematics- Chapter 7 -Exercise 7.11 ( Definite Integrals using properties) are given below.

Integration is an inverse process of differentiation. So integration is also known as anti-differentiation.

The solutions are given in simple steps.

A symbol ∫ represents integrals and C represents the integration constant.

All functions are not differentiable. Similarly, all functions are not integrable.

When a polynomial function P is differentiated, the result is a polynomial whose degree is 1 less than the degree of P. When a polynomial function P is integrated, the result is a polynomial whose degree is 1 more than P.

The derivative is used for finding some physical quantities like the velocity of a moving particle when the distance traversed at any time t is known. Similarly, the integral is used in calculating the distance traversed when the velocity at time t is known.

The process of finding functions whose derivative is given is called anti-differentiation or integration.

The two types of integrals i.e. indefinite integrals and definite integrals are connected by the fundamental theorem of integral calculus, which makes definite integrals as a practical tool for sciences, engineering, and many other disciplines like economics and probability.

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CBSE    Class 12   NCERT Solutions    Mathematics

Inverse Trigonometric Functions

Determinants – Chapter 4

Determinants Chapter 4 Exercise 4.1 and 4.2

Determinants Chapter 4 Exercise 4.3 and 4.4

Determinants – Chapter 4 – Exercise 4.5

Determinants – Chapter 4 – Exercise Miscellaneous

Continuity and Differentiability – Chapter 5

Continuity and Differentiability – Chapter 5 – Exercise 5.2

Continuity and Differentiability – Chapter 5 – Exercise 5.3

Continuity and Differentiability – Chapter 5 – Exercise 5.4

Continuity and Differentiability – Chapter 5 – Exercise 5.5

Continuity and Differentiability – Chapter 5 – Exercise 5.6

Continuity and Differentiability – Chapter 5 – Exercise 5.7

Integrals – Chapter 7

Integrals – Chapter 7 – Exercise 7.1

Integrals – Chapter 7 – Exercise 7.2 – Integration by substitution

Integrals – Chapter 7 – Exercise 7.3 – Integrations using trigonometric identities

Integrals – Chapter 7- Exercise 7.4

Integrals – Chapter 7 – Exercise 7.5 – Integration by partial Fractions

Integrals –Chapter 7 – Exercise 7.6 – Integration by parts

Integrals – Chapter 7- Exercise 7.7 – Some special types of standard integrals

Integrals – Chapter 7 – Exercise 7.9 – Definite Integrals

Integrals – Chapter 7 – Exercise 7.10 – Definite Integrals by substitution

Integrals – Chapter 7 – Exercise 7.11 – Definite Integrals using Properties

 

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 Definite Integrals using Properties – NCERT Solutions – Class 12 – Mathematics – Chapter 7 – Exercise 7.11

XII M NCERT Integrals Exercise 7.11 (1) XII M NCERT Integrals Exercise 7.11 (2) XII M NCERT Integrals Exercise 7.11 (3) XII M NCERT Integrals Exercise 7.11 (4) XII M NCERT Integrals Exercise 7.11 (5) XII M NCERT Integrals Exercise 7.11 (6) XII M NCERT Integrals Exercise 7.11 (7) XII M NCERT Integrals Exercise 7.11 (8) XII M NCERT Integrals Exercise 7.11 (9) XII M NCERT Integrals Exercise 7.11 (10)

CBSE    Class 12   NCERT Solutions    Mathematics

Inverse Trigonometric Functions

Determinants – Chapter 4

Determinants Chapter 4 Exercise 4.1 and 4.2

Determinants Chapter 4 Exercise 4.3 and 4.4

Determinants – Chapter 4 – Exercise 4.5

Determinants – Chapter 4 – Exercise Miscellaneous

Continuity and Differentiability – Chapter 5

Continuity and Differentiability – Chapter 5 – Exercise 5.2

Continuity and Differentiability – Chapter 5 – Exercise 5.3

Continuity and Differentiability – Chapter 5 – Exercise 5.4

Continuity and Differentiability – Chapter 5 – Exercise 5.5

Continuity and Differentiability – Chapter 5 – Exercise 5.6

Continuity and Differentiability – Chapter 5 – Exercise 5.7

Integrals – Chapter 7

Integrals – Chapter 7 – Exercise 7.1

Integrals – Chapter 7 – Exercise 7.2 – Integration by substitution

Integrals – Chapter 7 – Exercise 7.3 – Integrations using trigonometric identities

Integrals – Chapter 7- Exercise 7.4

Integrals – Chapter 7 – Exercise 7.5 – Integration by partial Fractions

Integrals –Chapter 7 – Exercise 7.6 – Integration by parts

Integrals – Chapter 7- Exercise 7.7 – Some special types of standard integrals

Integrals – Chapter 7 – Exercise 7.9 – Definite Integrals

Integrals –Chapter 7- Exercise 7.10-  Definite Integrals by Substitution

Integrals – Chapter 7 – Exercise 7.11 – Definite Integrals using Properties

 

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ISC              Class 12                   Mathematics Previous Years Board Questions Solutions of Previous years Board Questions Inverse Trigonometric Functions (2000 to Sem 1-2021) Inverse Trigonometric Functions (2000 to Sem 1-2021) Matrices (2000 to Sem 1 – 2021) Matrices (2000 to Sem 1-2021) Determinants (2000 to Sem1-2021) Determinants (2000 to Sem1-2021) Differentiation (2000 to Sem 1- 2021) Differentiation (2000 to Sem 1- 2021) L’ Hospital’s Rule (2001 to Sem1-2021) L’ Hospital’s Rule (2001 to Sem1-2021) Rolle’s Theorem and Lagrange’s Mean Value Theorem (1998 to 2020) Rolle’s Theorem and Lagrange’s Mean Value Theorems (1998 to 2020) Maxima and Minima (2000 to 2020) Maxima and Minima (2000 to 2020) Integration (1990 – 2011) Integration (1990 – 2011) Integration (2012 to 2022) Integration (2012 to 2022) Differential Equations (1991 to 2005) Differential Equations (1991 to 2005) Differential Equations (2006 to 2022) Differential Equations (2006 to 2022) Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2022) Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Linear Programming (2008 to Sem 2-2022) Linear Programming (2008 to 2022) Linear Regression (2005 to 2022)

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MCQ              Class 12         Mathematics Relations and Functions Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Tangents and Normals Maxima and Minima Increasing and Decreasing Functions Application of Calculus in Commerce and Economics (Set I) Application of Calculus in Commerce and Economics (Set II) Integration MCQs (Set 1)  Integration MCQs (Set 2) Specimen Paper for Semester 1 – 2021 – ISC – Class XII Mathematics Linear Regression

ISC   –   Class 12  –  Mathematics  –  Sem 2  –  2022  – Sample Paper                             Sample Paper 1                             Sample Paper 2

ISC – Class 12 –  Mathematics – Sem 1 – 2021 – Sample Paper                          Specimen Paper

ISC- Class 12 – Mathematics – Sem 2 – 2022 – Chapterwise Questions                       Differential Equations (Set 1)                       Differential equations (Set 2)                       Integration                      Probability                      Linear Programming (LPP)

ICSE – Class 10  -Mathematics   –     Sem 2  –    2022 – Sample Paper                               Sample Paper 1                Solutions of Sample Paper 1

ICSE – Class 10 – Mathematics –  Sem 1-  2021 – Sample Paper Mock Question Paper

 

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MCQ               Class 10            Mathematics Banking (Set 1) Banking (Set 2) GST Linear Inequations (Set 1) Linear Inequations (Set 2) Quadratic Equations Factorization Ratio and Proportion Matrices Arithmetic Progression (A.P.) Similarity (Set 1) Similarity (Set 2)  Reflection Section Formula  Straight Lines  Probability Circle (Set 1) Circle (Set 2) Mock Question Paper for Semester 1 (2021) ICSE Class X Mathematics ICSE Class X – Specimen Question Paper released by CISCE for Semester 1 (2021) – Mathematics

 

MCQ         Class 10      Physics Sound

 

Formula             Mathematics Formula and Theorems for Class X Class XI Formula Trigonometry Inverse Trigonometric Functions – Class 12   Differentiation and Limits for Class 11 and 12   Integration for Class 11 and 12    Linear Regression – Class 12- ISC

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