Integrals: Class 12 Mathematics (CBSE) important questions and practice
Integrals is chapter 7 of 13 in CBSE Class 12 Mathematics. Below are the topics the paper draws from, the question types that come up again and again, and a free practice test on this chapter alone.
Topics in this chapter
- Integration as the inverse of differentiation; standard integrals
- Integration by substitution
- Integration using partial fractions
- Integration by parts and the e^x[f(x) + f'(x)] form
- Standard integrals of the forms 1/(x^2 + a^2), 1/root(a^2 - x^2), root(x^2 + a^2) etc.
- Definite integrals: fundamental theorem and properties
What examiners usually ask
- Evaluate the integral of (x^2 + 1)/((x - 1)^2 (x + 3)) dx using partial fractions
- Evaluate the integral of e^x (sin x) dx by parts
- Evaluate the definite integral from 0 to pi/2 of (sin x)/(sin x + cos x) dx using properties
Exam tip
Memorise the standard integral table and the property integral from 0 to a of f(x) = integral of f(a - x), which solves most definite integral questions; write 'let x = ...' substitutions clearly and change limits for definite integrals.
Integrals on other boards and exams
Frequently asked questions
What are the important questions from Integrals for CBSE Class 12?
The question types listed above repeat most often in CBSE Class 12 Mathematics papers for this chapter. Practise them with the chapter test and then attempt them inside a full previous-year paper under time.
Is Integrals in the CBSE Class 12 Mathematics syllabus?
Yes. Integrals is part of the current CBSE Class 12 Mathematics syllabus, as listed on this site from the prescribed textbook.
Can I practise Integrals MCQs in Hindi?
Yes. The chapter test and explanations are available in Hindi and English, with an AI doubt solver for any question.