Maths · Class 12 · Chapter 7
Integrals
13 lessons 109 min 2 simulations
Integration runs differentiation backwards: given a rate of change, recover the function that produced it. The chapter first builds the indefinite integral, a whole family F(x) + C, and a toolkit for finding it (a table of standard results, substitution, trigonometric identities, partial fractions and integration by parts). It then turns to the definite integral, a single number that measures signed area, and links the two through the fundamental theorem of calculus and a set of properties that make many definite integrals short.
What the exam asks
JEE Main tests speed with the standard forms: spotting the right substitution, splitting a rational function into partial fractions, choosing the first function in integration by parts and recognising eˣ[f(x) + f′(x)]. Definite integrals are asked through the properties, above all the a + b − x trick, the even/odd rule and splitting at the points where a modulus changes sign. Marks are lost by forgetting + C, by not changing the limits after a substitution and by integrating straight across a point where the integrand is undefined.
Lessons
13 lessons · 109 min
1Antiderivatives and the constant CNCERT §7.1–7.211 min 1 sim2Standard integralsNCERT §7.26 min3Properties of the indefinite integralNCERT §7.2.16 min4Integration by substitutionNCERT §7.3.18 min5Using trigonometric identitiesNCERT §7.3.27 min6Integrals of some particular functionsNCERT §7.47 min7Partial fractionsNCERT §7.57 min8Integration by partsNCERT §7.68 min9Exponential pairs and square-root formsNCERT §7.6.1–7.6.27 min10The definite integral and the fundamental theoremNCERT §7.7–7.811 min 1 sim11Substitution in definite integralsNCERT §7.97 min12Properties of definite integralsNCERT §7.108 min13Chapter reviewMust-know facts, traps and formulas16 min