Integration by Parts
Definition
Integration by parts is a technique used to find the integral of a product of two functions. It involves using the formula ∫u dv = uv - ∫v du, where u and v are chosen functions.
Analogy
Integration by parts is like peeling an onion. You start with a whole onion (the original function) and peel off one layer at a time (integrating one part while differentiating the other), until you reach the core (the final integral).
Related terms
Partial Fractions: A method used to decompose a rational function into simpler fractions. It is often used in integration problems involving fractions.
Chain Rule: A rule in calculus that allows you to differentiate composite functions. It is the reverse process of integration by parts.
Tabular Integration: A systematic method for integrating products of functions repeatedly using a table. It can be helpful when integration by parts needs to be applied multiple times.
"Integration by Parts" appears in:
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Practice Questions (13)
Integration by parts can be used to evaluate integrals when the integrand is a product of two functions. Which of the following formulas represents integration by parts?
When should integration by parts be used?
In what situation would you need to use integration by parts a second time?
How many times should you use integration by parts to obtain your answer?
What is an example of a problem that you would need to solve using integration by parts?
When using integration by parts, how do you choose which portion of the integrand to be your f(x)?
When using integration by parts, how do you choose which portion of the integrand to be your g(x)?
When using integration by parts, when would you need to use additional algebra to get your final answer?
Solve the following problem using integration by parts: ∫x * e^x dx. What is the correct answer?
Solve the following problem using integration by parts: ∫ln(x) dx. What is the correct answer?
Solve the following problem using integration by parts: ∫x * sin(x) dx. What is the correct answer?
Solve the following problem using integration by parts: ∫x^2 * cos(x) dx. What is the correct answer?
Solve the following problem using integration by parts: ∫x * e^(2x) dx. What is the correct answer?
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