Integration- Previous Years Board Questions (2020 to 2023) with Solutions of ISC Class 12 Mathematics

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Solutions of ISC  Class 12 Mathematics Board Questions (2020 to 2023) on integration 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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XII M B Q S ISC Integration (2020 to 2023)1 XII M B Q S ISC Integration (2020 to 2023)2 XII M B Q S ISC Integration (2020 to 2023)3 XII M B Q S ISC Integration (2020 to 2023)4 XII M B Q S ISC Integration (2020 to 2023)5 XII M B Q S ISC Integration (2020 to 2023)6
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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)
Inverse Trigonometric Functions – (2020 to 2023)
 Inverse Trigonometric Functions – (2020 to 2023) 
Matrices (2000 to Sem 1 – 2021) Matrices (2000 to Sem 1-2021)
Matrices –(2020 to 2023)
 Matrices- (2020 to 2023)
Determinants (2000 to Sem1-2021) Determinants (2000 to Sem1-2021)
Determinants (2020 to 2023)
Determinants (2020 to 2023)
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)
Integration (2020 to 2023) Integration (2020 to 2023)
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 2013)
 Linear Regression – (2005 to 2013)
 Linear Regression (2014 to 2022) Linear Regression –  (2014 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

 

 Chapterwise Model Questions   –  Class 12 – Mathematics
Matrices (Set1)
Determinants

 

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)

 

            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

 

     ISC / ICSE  Board Paper

ISC  – Class 12 – 2020 – Mathematics Question Paper
ISC –  Class 12 – 2019 –  Mathematics Question Paper
ISC Class 12 Semester 1- 2021 Mathematics Question Paper with Solution
ISC – Class 12 – Semester 2-2022 Mathematics Question Paper with Solution
ICSE – Class 10 – 2020- Mathematics Question Paper 
ICSE – Class 10 – 2019 – Mathematics Question Paper
ICSE – Class 10 – 2018 – Mathematics Question Paper
ICSE – Class 10 – 2019 – Physics Question Paper
ICSE – Class 10 – 2018 – Physics Question Paper 
ICSE – Class 10 -2020- Mathematics Question PaperSolutions
ICSE – Class 10 – 2023 Mathematics Question Paper – Solutions

 

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