Integration is the reverse process of differentiation.

By differentiation, we find the derivative of the given function, whereas by integration we find the function whose derivative is known. The function is called the integral of the given function.

The process of determining an integral of a function is called the integration and the function to be integrated called the integrand.

The letter x in dx denotes that the integration is to be performed with respect to the variables x.

Integration  By Parts:

Aid to memory: If two functions are of different types, take the first function that comes first in the word ‘ILATE’ where 

(i) I stands for inverse trigonometric functions.

(ii) L stands for the logarithmic functions.

(iii)  A stands for algebraic functions.

(iv)  T stands for the trigonometric functions.

(v) E stands for the exponential functions.

 

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 2013)  Linear Regression – (2005 to 2013)  Linear Regression (2014 to 2022) Linear Regression –  (2014 to 2022)   Tapati’s Classes Online LIVE Mathematics Tuition by Tapati Sarkar Class 8 to 12 (ICSE, ISC) – Two days per week Contact: tapatisclasses@gmail.com

XII M B Q S Integration (2012 to 2022)1 S ISC Integration (2012 - 2020) 2 S ISC Integration (2012 - 2020) 3 S ISC Integration (2012 - 2020) 4 S ISC Integration (2012 - 2020) 5 S ISC Integration (2012 - 2020) 6 S ISC Integration (2012 - 2020) 7 S ISC Integration (2012 - 2020) 8 S ISC Integration (2012 - 2020) 9 S ISC Integration (2012 - 2020) 10 S ISC Integration (2012 - 2020) 11 XII M B Q S Integration (2012 to 2022)12 XII M B Q S Integration (2012 to 2022)13 XII M B Q S Integration (2012 to 2022) 14

ISC              Class 12                   Mathematics Previous Years Board Questions Solutions of Previous years Board Questions Inverse Trigonometric Functions (2000 to 2020) Inverse Trigonometric Functions (2000 to 2020) Matrices (2000 to 2020) Matrices (2000 to 2020) Determinants (2000 to 2020) Determinants (2000 to 2020) Differentiation (2000 to 2020) Differentiation (2000 to 2020) 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 2020) Integration (2012 to 2020) Differential Equations (1991 to 2005) Differential Equations (1991 to 2005) Differential Equations (2006 to 2020) Differential Equations (2006 to 2020) Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2020) Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2020) Probability (Baye’s Theorem) (2000 to 2019) Probability (Baye’s Theorem) (2000 to 2019) 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 2020) Application of Calculus in Commerce and Economics (2005 to 2020) Linear Programming (2008 to 2020) Linear Programming (2008 to 2020) Linear Regression (2005 to 2013) Linear Regression – (2005 to 2013) Linear Regression (2014 to 2022) Linear Regression –  (2014 to 2022)

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

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

 

 

ISC / ICSE  Board Paper ISC  – Class 12 – 2020 – Mathematics Question Paper ISC –  Class 12 – 2019 –  Mathematics Question Paper 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 Paper– Solutions

 

 

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