Maths

Definite integration involves finding the integral of a function over a specific interval. This process yields a number that represents the net area under the curve of the function between the two endpoints of the interval. Here are some fundamental formulas and properties related to definite integrals: Fundamental Theorem of Calculus The Fundamental Theorem of […]

Distance Formula For two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) in the Cartesian plane, the distance between them is given by: \[D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\] Section Formula For two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), the coordinates ( (x, y) ) of a point ( P

A periodic function is a mathematical function that repeats its values in a predictable pattern over a specific interval. This interval is known as the period of the function. In other words, if you were to graph a periodic function, you would observe the same pattern repeating at regular intervals Definition of Periodic Function A

The Central Board of Secondary Education (CBSE) is one of the oldest and most preferred educational board in India. The board conducts the final examination for Class 10 and 12 along with various other competitive examinations. CBSE aims to provide a quality education to all its learners so that they can succeed in their future.

The integration of odd function over a symmetric interval can be understood through some fundamental concepts in calculus and symmetry. An odd function is defined as a function $f(x)$ that satisfies the condition $f(-x) = -f(x)$ for all $x$ in the domain of the function. Graphically, odd functions exhibit symmetry about the origin, meaning their

Here is the CBSE Class 12 Maths Syllabus CLASS XII (Total Periods 240) UNIT I: RELATIONS AND FUNCTIONS Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. UNIT II: ALGEBRA Concept, notation, order, equality, types of matrices, zero

Integration of inverse trigonometric functions can be calculated using integration by parts ,integration by substitution .Here are the formula for it \[ \int \sin^{-1}x \, dx = x \sin^{-1}x + \sqrt{1 – x^2} + C \] \[ \int \cos^{-1}x \, dx = x \cos^{-1}x – \sqrt{1 – x^2} + C \] \[ \int \tan^{-1}x \,

Introduction The integration of irrational functions, which involves incorporating radicals (or root functions) into the integrand, is a challenging yet intriguing area of calculus. These functions often contain variables under a square root or higher-order roots, such as $\sqrt{x}$, $\sqrt[3]{x^2 + 1}$, and similar forms. This article delves into the methods and applications of integrating