How to Find Integration by Part?
Integration by part is used to find the integration of the product of two functions. We can achieve this using the steps discussed below,
Suppose we have to simplify ∫uv dx
Step 1: Choose the first and the second function according to the ILATE rule. Suppose we take u as the first function and v as the second function.
Step 2: Differentiate u(x) with respect to x that is, Evaluate du/dx.
Step 3: Integrate v(x) with respect to x that is, Evaluate ∫v dx.
Use the results obtained in Step 1 and Step 2 in the formula,
∫uv dx = u∫v dx − ∫((du/dx)∫v dx) dx
Step 4: Simplify the above formula to get the required 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