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What is the purpose of finding derivative?
The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
What is a integration?
the process of finding a function whose derivative is a given function
What is the difference between integration and anti-derivatives?
An integral and an anti-derivative are the same thing. Integration means the process of finding the integral, just as anti-differentiation means the process of finding the anti-derivative.
How does one do integration by parts?
Integration by parts is the integration of the product rule of differentiation. Used to transform a non-simple derivative integral into a simple antiderivative integral.
Why a constant is written after integrating?
Integration is the opposite of differentiation (taking the derivative). The derivative of a constant is zero. Integration is also called antidifferentiation since integration and differentiation are opposites of each other. The derivative of x^2 is 2x. The antiderivative (integral) of 2x is x^2. However, the derivative of x^2 + 7 is also 2x. Therefore, the antiderivative of 2x is x^2 + C, in general, where the constant C has to be determined from the context of the problem. In the above case, the constant happens to be C=7. We use integration to solve first order differential equations. When solving first order differential equations, like in "word problems", you must determine the integration constant using the initial conditions (ie the conditions we know to be true at t=0 - we usually know what these are), or the boundary conditions (ie the conditions we know to be true at x=0 and y=0).
Why does an answer to an integration problem involve a Constant of Integration?
The indefinite integral is the anti-derivative - so the question is, "What function has this given function as a derivative". And if you add a constant to a function, the derivative of the function doesn't change. Thus, for example, if the derivative is y' = 2x, the original function might be y = x squared. However, any function of the form y = x squared + c (for any constant c) also has the SAME derivative (2x in this case). Therefore, to completely specify all possible solutions, this constant should be added.
What is difference between anti integration and derivative?
In all but very exceptional cases there is no difference.
What is the anti derivative of x squared plus x?
The anti-derivative of X2 plus X is the same as the anti-derivative of X2 plus the anti-derivative of X. The anti derivative of X2 is X3/3 plus an integration constant C1 The anti derivative of X is X2/2 plus an integration constant C2 So the anti-derivative of X2+X is (X3/3)+(X2/2)+C1+C2 The constants can be combined and the fraction can combined by using a common denominator leaving (2X3/6)+(3X2/6)+C X2/6 can be factored out leaving (X2/6)(2X+3)+C Hope that helps
Relationship between Integration and differentiation?
Integration and differentiation effectively un-do each other. The derivative of the integral of a function is usually the original function. The reverse is also true, to a point.
What is integration in mathematics?
Opposite of differentiation. Given the rate of change of something (for example, speed [which is rate of change of position] ) which might vary according to some formula, then integration is a way of calculating the total distance after a specified interval.
What word means the opposite of segregation?
inclusion INTEGRATION! :o)
What is the relationship of integral and differential calculus?
We say function F is an anti derivative, or indefinite integral of f if F' = f. Also, if f has an anti-derivative and is integrable on interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a) Thirdly, Let F(x) be the definite integral of integrable function f from a to x for all x in [a, b] of f, then F is an anti-derivative of f on [a,b] The definition of indefinite integral as anti-derivative, and the relation of definite integral with anti-derivative, we can conclude that integration and differentiation can be considered as two opposite operations.
