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  1. Learning Paths
  2. /Mathematics · High School (11–12)
  3. /Integrals
Mathematics
High School (11–12)
Functions and Calculus › IntegralsChapter 11Contains Standard content

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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Courses in This Path (4)

1.
Integration as the Reverse of Differentiation
You know that the derivative of x2x^2x2 is 2x2x2x. Now go the other way: which function has the derivative 2x2x2x
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More onFunctions and Calculus › Integrals

Mathematics · High School (11–12)

  1. 1Functions and Their Graphs
  2. 2Trigonometric Functions
  3. 3Complex Numbers and Quadratic Equations
  4. 4Permutations and Combinations
  5. 5Sequences and Series
? 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.
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2.
Methods of Integration
Some integrals do not yield to substitution alone. Learn the integrals of the special forms, including those with a quadratic under a root, split a fraction into partial fractions, and use integration by parts, which comes from the product rule. Choose the right method by looking at the shape of the integrand. It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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3.
Definite Integrals
How much distance does a bus cover if you know its speed at every moment? The answer is the area under the speed graph. Meet the area function, see why its derivative is the original function, and use the Fundamental Theorem of Calculus to evaluate definite integrals. Then use substitution and the properties of definite integrals, and see the integral as the limit of a sum. It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
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4.
Integration in Depth: Reduction Formulas and Limits of SumsStandard
Beyond the textbook. Build reduction formulas that bring a hard integral down to an easy one, use the symmetry properties on harder integrals, and turn limits of sums into integrals. Then compare integrals without evaluating them, and differentiate an integral whose limits depend on xxx. It is at the level of JEE Advanced, A-Level Further Maths and IB Higher Level, with a full timed paper.
3 lessons · 12 problems · 2 Python labs · 1 question set · 1 mock test
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6
Straight Lines
  • 7Binomial Theorem
  • 8Matrices and Determinants
  • 9Continuity and Differentiability
  • 10Applications of Derivatives
  • 11IntegralsYou are here
  • 12Applications of Integrals
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    Mathematics
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