Maths

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 A function is said […]

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 \,

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

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

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

Number 64 is a composite number and we will find how to find the factors of 64. We will also see techniques to find out the Prime factorization of 64 easily Factors of 64 A factor of a number is an exact divisor of that number. So factors of 64 are the numbers which are