How do you Calculate Percentages?https://www.youtube.com/watch?v=sYNF8MBKJpIPercentageWhen we take 100 as the denominator of fractions, the numerators are called percentages. For convenience, the symbol % is used for percent. When we take 100 as the den…

How to Find the Median ValueThe median is the central value of the set of observations provided all the observations are arranged in the ascending or descending orders. It is generally used, when effect of extreme items is to be kept out. Example: The me…

Integration by SubstitutionIntegration by Substitution(1) When integrand is a function i.e.,∫f[?(x)] ?'(x) dx: Here, we put ?(x)=t, so that ?'(x) dx=dt and in that case the integrand is reduced to ∫f(t) dt. (2) When integrand is the product of two factor…

ParabolaA parabola is the locus of a point which moves in a plane such that its distance from a fixed point (i.e., focus) in the plane is always equal to its distance from a fixed straight line (i.e., directrix) in the same plane. Standard equation of …

What is the De’ Moivre’s Theorem?(1) If n is any rational number, then (cos θ + i sin θ)n = cos nθ + i sin nθ. (2) If z = (cos θ1 + i sin θ1) (cos θ2 + i sin θ2) (cos θ3 + i sin θ3)………… (cos θn + i sin θn) then z = cos (θ1 + θ2 + θ3 + ……… + θn) + i sin …

Determinant of a Matrix Determinant Let us consider three homogeneous linear equations a1x + b1y + c1z = 0, a2x + b2y + c2z = 0 and a3x + b3y + c3z = 0 Eliminated x, y, z from above three equations we obtain a1(b2c3 − b3c2) − b1(a2c3 –a3c2) + (a2b3 – a3…

Probability – Types of EventsEvent: An event is a subset of a sample space. Simple event: An event containing only a single sample point is called an elementary or simple event.Compound events: Events obtained by combining together two or more elementary…

Integration Rules and FormulasIntegral of a FunctionA function ϕ(x) is called a primitive or an antiderivative of a function f(x), if ?'(x) = f(x). Let f(x) be a function. Then the collection of all its primitives is called the indefinite integral of f(…

PolynomialsAlgebraic expression containing many terms of the form axn, n being a non-negative integer is called a polynomial. i.e., f(x) = a0 + a1x + a2x2 + a3x3 + …….. + an-1xn-1 + anxn, where x is a variable, a0, a1, a2, …… an are constants and an ≠ 0.…

Definite IntegralsLet ?(x) be the primitive or anti-derivative of a function f(x) defined on [a, b] i.e., \(\frac { d }{ dx } [\phi (x)]=f(x)\). Then the definite integral of f(x) over [a,b] is denoted by \(\int _{ a }^{ b }{ f(x)dx }\) and is defined a…