Maths

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

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

We can easily find the integration of $\frac {1}{1+ cos x}$ and $\frac {1}{1 -cos x}$ using trigonometric identities and fundamental integration techniques, The formula of these integral is given as $\int \frac {1}{1+ cos x} \; dx = \tan \frac {x}{2} + C$ or $\int \frac {1}{1+ cos x} \; dx = -\cot x

The integration of tan cube x $\tan ^3 x$, can be found using integration substitution and trigonometry identities . The integral of $\tan ^3 x$ with respect to (x) is: \[\int \tan^3 x \, dx =\frac {1}{2} \tan^2 x – \ln |sec x|+ C\] Here, (C) represents the constant of integration, which is added because