Antiderivatives Index

Definite Integral

Definite Integral: Definite integral is a form of Integral or Anti derivative in which we don’t get a range of answer or indefinite answer , Instead we get a fixed or definite answer. Or, A definite integral is the integral of a function in a closed interval and it is denoted by: Which means , the Integral or Anti derivative of the function “f(x)” in an interval from “a” to “b”. Definite Integral Formula: We can calculate or evaluate a definite integral using the definite integral formula which...

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Integration by Parts

Integration by Parts is a powerful tool and one of the best , most used techniques of integration used to evaluate integrals. The main formula used in  integration by parts is: This formulas is derived from the product rule for differentiation as: Multiplying both side of product rule formula by or , Now integrating both side of above equation we get: This formulas converts the problem of integrating a function with respect to another ( u .dv ) into the problem  of integrating second function with respect to first function ( v .du). So...

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Integration by trigonometric substitution

Integration by trigonometric substitution

integration by trigonometric substitution: One of the most powerful techniques of integration is Integration by trigonometric substitution. Integration by  trigonometric substitution is similar technique to integration by substitution . In integration by trigonometric substitution we substitute a variable by another trigonometrical variable. We can integrate the integrals which involves , or . It is obvious that substitution turns into ; the substitution turns into into and the substitution turns into  . These substitutions makes...

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Integration by Substitution

Integration by Substitution: Integration can be easily done by using  integration formulas , If the integral is in the standard form where we can easily apply formulas. But if the function which is to be integrated is not in the standard form then it is either harder or impossible to use integration formulas to integrate. In that case we need to to use Integration by Substitution method to integrate a given function. In the method of Integration by substitution , We reduce a integral in non-standard form into a integral  in standard form...

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Techniques of Integration

To find the antiderivative (Integral ) we use certain techniques and tricks , which makes it easier to integrate a given function . Such techniques used to find integral of a function effectively is called techniques of integration. There are many techniques and tricks of integration. Some the main techniques of integration are: Techniques of integration: 1. By using Integration Formulas. 2. Integration by Substitution. 3. Integration by Trigonometrical Substitution. 4. Integration by...

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Antiderivatives ( Indefinite Integrals)

Antiderivatives or Indefinite integrals: If , “f” is a continuous function defined on an open interval (a,b) ; Then the function “F” ( function F is capital “f”) is called antiderivative of function “f”, if the derivative of function “f” is function “F” on the interval. Or , If , then , The function is said to be antiderivative of function . But as the derivative of constant is zero. Not only , but is also the antiderivative of function where , “c” is...

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