Antiderivative formula proof graphical analysis

#Antiderivative formula proof graphical analysis how to

в€«-f(x)dx = -в€«f(x)dx, This property can be thought as a special case of the previous property with k = -1.

в€«kf(x)dx = k в€«f(x)dx, here вЂњkвЂќ is any constant.

There are some important properties that come in handy while calculating the anti-derivatives for the functions. Here the symbolВ в€« denotes the anti-derivative operator, it is called indefinite integrals.

If F(x), is the anti-derivative of f(x) then the most general anti-derivative of f(x) is called indefinite integral. This means,ДЇor, g(x) = 2x the anti-derivative will be,ДЄ function F is called anti-derivative of the function, if Since constant cancels out while differentiating, we can conclude that for any function f(x), there can infinitely many anti-derivative functions with different values of the constants. Also, in the case of another function h(x) = x 2 + 2, the derivative of this function is still g(x). Notice that while calculating the derivative, the exponent on the variable вЂњxвЂќ decreased by 1, so in case of the reverse process the exponent will be increased. Anti-Derivatives are supposed to generate the function f(x) given another function g(x). LetвЂ™s consider a function f(x) = x 2, on differentiating this function, the output is another function g(x) = 2x. It becomes essential to understand the concept and the methods for using anti-derivatives to generate the functions from their derivatives. In that case, anti-derivatives come to the rescue. Sometimes there are situations where the derivative is available, but no information is given about the function. Properties of Matrix Addition and Scalar Multiplication | Class 12 MathsДerivatives are the way to measure the rate of change, given a function f(x), the derivatives for that function calculate the rate of change of the value of that function at a particular point.Torque on an Electric Dipole in Uniform Electric Field.p-n Junction Diode- Definition, Formation, Characteristics, Applications.Class 12 NCERT Solutions - Mathematics Part I - Chapter 2 Inverse Trigonometric Functions - Exercise 2.1.Graphical Solution of Linear Programming Problems.Shortest Distance Between Two Lines in 3D Space | Class 12 Maths.Difference between write() and writelines() function in Python.Data Communication - Definition, Components, Types, Channels.

#Antiderivative formula proof graphical analysis how to

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