Integration Worksheet Integration Worksheet A function ?(x) is called an integral of a function f(x) if ?' (x) = f(x). 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 f(x) be a function. Then the family of all its primitives is called the indefinite integral of f(x) and is denoted by ∫f(x) 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 Descriptive Statistics Examples
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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 (∫ f(x) dx) = f(x), Read More About Compare and Contrast Rational And Irrational Numbers
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That is the differentiation of an integral is the integrand itself or differentiation and integration are inverse operation. ii) ∫ k f(x) = k ∫ f(x), where ‘k’ is constant. That is the integral of the product of a constant and a function = the constant * integral of the function. iii) ∫ f(x) +- g(x) = ∫ f(x) dx +- ∫ g(x) 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.
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