Integration Previous Years Board's Questions (1990 - 2011) (with Answers) of ISC Class 12 Mathematics

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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 integration and the

function to be integrated is called the integrand.

The letter x in dx denotes that the integration is to be performed

with respect to the variable x.

There are no hard and fast- rules for making suitable substitutions.

Practice will help you to acquire the necessary skill.

pdf (first page ) contains questions from the year 1990 to 1999.

The following guidelines will be useful.

(i) If the integrand contains $\sqrt{a^{2}-x^{2}}, \, \boldsymbol{\mathrm{put}}\, x=a\, sin\, \Theta$

(ii) If $\sqrt{x^{2}-a^{2}}$ occurs in the integrand, put $x= a sec\, \Theta$ .

(iii) If the integrand contains $a^{2}+x^{2}$ with the radical or power, put $x=a\, tan\, \Theta$ .

pdf (2nd page) contains questions from the year 2000 to 2006.

Integration by parts:

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

(i) where I stands for inverse trigonometric functions.

(ii) L stands for the logarithmic function.

(iii) A stands for the algebraic function.

(iv) T stands for the trigonometric functions.

(v) E stands for the exponential functions.

pdf (3rd page) contains questions from the year 2006 to 2011.

Aid to Memory: The rule of integration by parts is useful in integrating single functions like

logarithmic and inverse trigonometric functions.

For this unity (i.e., 1) is taken as the second function.

pdf (4th page) contains answers to the board questions.

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 2020)