Nabila Abdul-Alhadi Alsharif
An exploration of indefinite integrals and antiderivatives in calculus, defining them as the reverse of derivatives within a given interval. Learn how to find antiderivatives of functions and understand the constant of integration. Dive into the concepts of integral calculus, with detailed examples and explanations to deepen your understanding.
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Presentation Transcript
Indefinite Integral Indefinite Integral
Definition of Indefinite Integral A function F is called antiderivative (also an indefinite integral) of a function f in the interval I if = / ( ) ( ), F x f x x I = + ( ) ( ) , f x dx F x C constant is of integratio n where C
= + dx x C + 1 n x = + n , 1 x dx C n + 1 x n = + 1 ln x dx C + 1 n [ ( n )] + f f x = + n [ ( )] ( ) , 1 f x f x dx C n 1 x = + 1 [ ( )] ( ) ln ( ) f x f x dx C ( ) g x a = + ( ) g x l ( ) where , a is a constant a g x dx C ln ( ) a
