Integração por Partes (u,v)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
IPP
About this calculator
The Integration by Parts calculator is a useful tool for solving integrals that involve composite functions. It uses the formula ∫u dv = uv − ∫v du, which allows simplifying these integrals. This technique is fundamental in advanced calculus, as it helps solve problems that would otherwise be difficult to solve.
The Integration by Parts formula works by assigning the functions u and v to the parts of the integral. The correct choice of the functions u and v is crucial to the success of the integration. Typically, u is chosen as the function that becomes simpler when differentiated, and v as the function that becomes simpler when integrated.
The Integration by Parts calculator is useful in a variety of situations, such as solving physics, engineering, and economics problems. For example, in physics, it can be used to calculate the kinetic energy of a moving object. In engineering, it can be used to design complex systems.
When using the Integration by Parts calculator, it is essential to be careful with the choice of the functions u and v. Additionally, it is crucial to verify if the resulting integral is solvable. With practice and experience, you will become more skilled at applying this technique to solve complex problems.
Frequently asked questions
What is Integration by Parts?
Integration by Parts is a technique used to solve integrals that involve composite functions. It uses the formula ∫u dv = uv − ∫v du.
How to choose the functions u and v?
Typically, u is chosen as the function that becomes simpler when differentiated, and v as the function that becomes simpler when integrated.
What are the applications of Integration by Parts?
Integration by Parts has applications in physics, engineering, and economics, among other fields. It can be used to solve complex problems that involve integrals.
Why is it important to be careful with the choice of the functions u and v?
The correct choice of the functions u and v is crucial to the success of the integration. If the functions are chosen incorrectly, the resulting integral may be difficult or impossible to solve.
How to verify if the resulting integral is solvable?
It is essential to verify if the resulting integral is solvable before proceeding with the integration. This can be done by checking if the integral has a known solution or if it can be solved using other integration techniques.