What is Partial Integration?
Partial integration, also known as integration by parts, is a technique used in calculus to evaluate the integral of a product of two functions. The formula for partial integration is given by:
∫ u dv = uv – ∫ v du
Where u and v are differentiable functions of x. This formula allows us to simplify the integral of a product by breaking it down into two simpler integrals. The idea is to choose u and dv so that the new integral on the right-hand side is easier to evaluate than the original one on the left-hand side.
History of Partial Integration
Integration by part concept was first proposed by the famous Brook Taylor in his book in 1715. He wrote that we can find the integration of the product of two functions whose differentiation formulas exist.
Some important functions do not have integrations formulas and their integration is achieved using integration by part-taking them as a product of two functions. For example, ∫ln x dx can not be calculated using normal integration techniques. But we can integrate it using Integration by part technique and taking it as a product of two functions that is, ∫1.ln x dx.
Read More about Method of Integration.
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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