Integration by Parts
What is integration by parts?
Integration by parts is the technique for finding the integration of the product of the two functions where the normal techniques of integration fail. Integration by the part formula is the,
∫u.v dx = u ∫ v d(x) – ∫ [u’ {∫v dx} dx] dx + c
What is integration by parts formula?
For two functions f(x) and g(x) the integration by part formula is,
∫ f(x).g(x) dx = f(x) ∫ g(x) d(x) – ∫ [f'(x) {∫g(x) dx} dx] dx + c
where f'(x) is differentiation of f(x).
How to derive integration by parts formula?
Integration by part formula is derived using the product rule of differentiation.
Why do we use integration by parts formula?
Integration by part formula is used to find the integration of the function when the normal differentiation techniques fail. We can find the integration of inverse trigonometric functions, and logarithmic functions using Integration by part formula
What is the application of integration by parts?
Integration by part has various applications and the basic application of it is that it is used to find the integration of the function when the function is given as the product of the functions which can not be simplified further. For example ∫ f(x).g(x) dx is achieved using Integration by parts.
Integration by Parts
Integration by Parts: Integration by parts is a technique used in calculus to find the integral of the product of two functions. It’s essentially a reversal of the product rule for differentiation.
Integrating a function is not always easy sometimes we have to integrate a function that is the multiple of two or more functions in this case if we have to find the integration we have to use integration by part concept, which uses two products of two functions and tells us how to find their integration.
Now let’s learn about Integration by parts, its formula, derivation, and others in detail in this article.
Table of Content
- What is Integration by Parts?
- What is Partial Integration?
- Integration By Parts Formula
- Derivation of Integration By Parts Formula
- ILATE Rule
- How to Find Integration by Part?
- Repeated Integration by Parts
- Applications of Integration by Parts
- Integration by Parts Formulas
- Integration By Parts Examples
- Practice Problems
- FAQs
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