What is Integration by Parts?
Integration by part is the technique used to find the integration of the product of two or more functions where the integration can not be performed using normal techniques. Suppose we have two functions f(x) and g(x) and we have to find the integration of their product i.e., ∫ f(x).g(x) dx where it is not possible to further solve the product of this product f(x).g(x).
This integration is achieved using the formula:
∫ f(x).g(x) dx = f(x) ∫ g(x) d(x) – ∫ [f'(x) {∫g(x) dx} dx] dx + c
Where f'(x) is the first differentiation of f(x).
This formula is read as:
Integration of the First Function multiplied by the Second Function is equal to (First Function) multiplied by (Integration of Second Function) – Integration of (Differentiation of First Function multiplied by Integration of Second Function).
From the above formula, we can easily observe that choosing the first function and the second function is very important for the success of this formula, and how we choose the first function and the second function is discussed further in this article.
Read More about Integral Formula.
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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