NCERT Solutions for Class 12 Mathematics Chapter 7 Exercise 7.7 (Integrals) 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.

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 – Integration using trigonometric identities

Integrals – Chapter 7- Exercise 7.4 – Integrals of some Particular Functions

Integrals – Chapter 7 – Exercise 7.5 – Integration by Partial Fraction

Integrals – Chapter 7 – Exercise 7.6 – Integration by parts

Differential Equations –Chapter 9 – Exercise 9.4 – Differential Equations with Variable Separable

Differential Equations –Chapter 9 – Exercise 9.6 – First-Order Linear Differential Equations

 

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 NCERT Solutions – Class 12 – Mathematics – Integrals – Chapter 7 – Exercise 7.7  

Some special types of standard integrals 

XII M NCERT Integrals Exercise 7.7 (1) XII M NCERT Integrals Exercise 7.7 (2) XII M NCERT Integrals Exercise 7.7 (3) XII M NCERT Integrals Exercise 7.7 (4)

 

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 – Integration using trigonometric identities

Integrals – Chapter 7- Exercise 7.4 – Integrals of Some Particular Functions

Integrals – Chapter 7 – Exercise 7.5 – Integration by Partial Fraction

Integrals – Chapter 7- Exercise 7.6 – Integration by parts

Integrals – Chapter 7 – Exercise 7.7 – Some special type of standard integrals

Differential Equations –Chapter 9 – Exercise 9.4 – Differential Equations with Variable Separable

Differential Equations –Chapter 9 – Exercise 9.6 – First-Order Linear Differential Equations

 

Tapati’s Classes – Online LIVE  Mathematics Classes Live Online Mathematics Tuition by Tapati Sarkar Class 8 to 12 (ICSE, ISC)          –    Two days per week Contact: tapatisclasses@gmail.com

 

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 Sem 1-2021) Maxima and Minima (2000 to Sem 1 – 2021) 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)

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)

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