NCERT Solutions for Class 12 Maths – Exercise 7.9 – Chapter 7 – Integrals – Definite Integrals

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NCERT Solutions for Class 12 Mathematics Chapter 7 Exercise 7.9 (Definite 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 – 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
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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Definite Integrals  – NCERT Solutions – Class 12 – Mathematics – Chapter 7 – Exercise 7.9

XII M NCERT Integrals Exercise 7.9 (1) XII M NCERT Integrals Exercise 7.9 (2) XII M NCERT Integrals Exercise 7.9 (3) XII M NCERT Integrals Exercise 7.9 (4) XII M NCERT Integrals Exercise 7.9 (5) XII M NCERT Integrals Exercise 7.9 (6)
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
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
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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

 

Tapati’s Classes
Online LIVE Mathematics Tuition by Tapati Sarkar
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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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