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the integral is called an indefinite integral, which represents a class of functions (the antiderivative) whose derivative is the integrand. [19] The fundamental theorem of calculus relates the evaluation of definite integrals to indefinite integrals. There are several extensions of the notation for integrals to encompass integration on ...
JEE-Main, unlike JEE-Advanced, has a fixed exam structure and is not subject to change every year. Up until 2018, the JEE-Main Paper-I was three hours long and consisted of thirty questions in each of the three subjects (physics, chemistry and maths). 4 marks are awarded for correct answers and 1 mark is deducted for incorrect answers.
A candidate should have appeared for the Class XII (or equivalent) examination for the first time in either 2024 or 2025 with Physics, Chemistry, and Mathematics as compulsory subjects with a minimum of 75% aggregate marks or in the top 20 percentile in their 10+2 Board Examination conducted by their respective board for General,EWS and OBC ...
Sum rule in integration; Constant factor rule in integration; Linearity of integration; Arbitrary constant of integration; Cavalieri's quadrature formula; Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign ...
In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. [1] A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. [2]
[48]: 163–165 F is an indefinite integral of f when f is a derivative of F. (This use of lower- and upper-case letters for a function and its indefinite integral is common in calculus.) The definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the x-axis.
In mathematics, the definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} is the area of the region in the xy -plane bounded by the graph of f , the x -axis, and the lines x = a and x = b , such that area above the x -axis adds to the total, and that below the x -axis subtracts from the total.
In 2024, NTA reduced JEE Main syllabus to reduce pressure and stress among students and to meet the same syllabus structure as that of the NCERT revised books. In the latest 2025 Information brochure, the syllabus remained same as of 2024 but NTA reduced the number of question in Section - B of Paper - 1 (B.E/B-Tech) from 5 out 10 questions (to ...