Integrals

A tank fills at a rate that changes from minute to minute. You know the rate at every moment. How much water is in the tank after an hour? Integration answers this. It undoes differentiation, and it also measures the area under a graph. In this chapter you find antiderivatives, learn substitution, partial fractions and integration by parts, and then meet the definite integral and the Fundamental Theorem of Calculus. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python checks every integral on the computer.

Part of Mathematics · High School (11–12) (chapter 11)

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Integration as the Reverse of Differentiation

You know that the derivative of

x^2

2x

. Now go the other way: which function has the derivative

2x

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More onFunctions and Calculus › Integrals

? Find antiderivatives, understand the constant of integration, learn the standard integrals and the rules, and then use substitution, with the help of trigonometric identities, to reach integrals that look hard. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.