NCERT Solutions for Class 12 Maths Exercise 7.5 Chapter 7 – Integrals – Integration by Partial Fractions

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NCERT Solutions for Class 12 Mathematics Chapter 7 Exercise 7.5 (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.

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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 (1)
Differential Equations –Chapter 9 – Exercise 9.4 – Differential Equations with Variable Separable

 

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NCERT Solutions – Class 12 – Mathematics – Integrals – Chapter 7 – Exercise 7.5 – Integration by Partial Fractions

XII M NCERT Integrals Exercise 7.5 (1) XII M NCERT Integrals Exercise 7.5 (2) XII M NCERT Integrals Exercise 7.5 (3) XII M NCERT Integrals Exercise 7.5 (4) XII M NCERT Integrals Exercise 7.5 (5) XII M NCERT Integrals Exercise 7.5 (6) XII M NCERT Integrals Exercise 7.5 (7) XII M NCERT Integrals Exercise 7.5 (8) XII M NCERT Integrals Exercise 7.5 (9) XII M NCERT Integrals Exercise 7.5 (10) XII M NCERT Integrals Exercise 7.5 (11)
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 substituion
Integrals – Chapter 7 – Exercise 7.3 – Integration 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
Differential Equations –Chapter 9 – Exercise 9.4 – Differential Equations with Variable Separable

 

Tapati’s Classes
Online LIVE Mathematics Tuition by Tapati Sarkar
Class 8 to 12 (ICSE, ISC, CBSE) – Two days per week
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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 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)
 

 

Tapati’s Classes
Online LIVE Mathematics Tuition by Tapati Sarkar
Class 8 to 12 (ICSE, ISC, CBSE) – Two days per week
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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

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