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integration worksheet integration worksheet a function x is called an integral of a function fx if x fx for example x4 4 is a primitive of x3 because d /dx x4 4 x3 indefinite integral is one of the types of integration the definition of indefinite integrals is that let fx be a function then the family of all its primitives is called the indefinite integral of fx and is denoted by fx dx the process of finding an indefinite integral of a given function is called integration of the function integration worksheet can be solved by following fundamental rules i d dx xn 1 n 1 x n n -1 x n dx x n 1 n 1 c n -1 ii d dx log x 1 x 1 x dx log x c iii d dx cos x sin x sin x dx -cos x c know more about associative property of rational numbers tutorcircle.com page no 1/4

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iv d dx sin x cos x cos x dx sin x c v d dx tan x sec2x sec2 x dx tan x c vi d dx log sin x cot x cot x dx log sin x c vii d dx sec x sec x tan x sec x tan x dx sec x c viii d dx log cosec x ­ cot x cosec x dx log cosec x ­ cot x c the list of integration formulas is very long so it is not possible to list all of them here there are three methods of integration integration by substitution the method of evaluating an integral by reducing it to standard form by a proper substitution is called the integration by substitution integration by parts in this method we divide the function into two parts integration of rational algebraic functions by using partial function integration is the reverse process of the differentiation or we can say that integration is the opposite of the differentiation means they are opposite to each other either it is integration or differentiation but the similarity is that both the operation is linear some standard results on the integration are theorem i d dx fx dx fx read more about compound events worksheets tutorcircle.com page no 2/4

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that is the differentiation of an integral is the integrand itself or differentiation and integration are inverse operation ii k fx k fx where `k is constant that is the integral of the product of a constant and a function the constant integral of the function iii fx gx fx dx gx dx that is the integral of the sum or difference of a finite number of functions is equal to the sum or difference of the integrals of the various functions tutorcircle.com page no 3/4 page no 2/3

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thank you for watching presentation

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