Questions and Answers
What is the purpose of integration by parts?
To transform the antiderivative of a product of functions into an antiderivative for which a solution can be more easily found
How is integration by parts related to the product rule of differentiation?
It is derived using the product rule
Who discovered integration by parts?
Brook Taylor
For which type of integrals does a more general formulation of integration by parts exist?
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What is the discrete analogue for sequences of integration by parts called?
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Study Notes
Integration by Parts
- The purpose of integration by parts is to integrate products of functions by transforming them into easier integrals or integrals that can be evaluated more easily.
Relationship to Product Rule
- Integration by parts is related to the product rule of differentiation, as it can be seen as the inverse operation of the product rule.
History
- The discovery of integration by parts is attributed to Scottish mathematician Brook Taylor.
General Formulation
- A more general formulation of integration by parts exists for integrating functions with multiple variables, such as multivariate functions.
Discrete Analogue
- The discrete analogue for sequences of integration by parts is called summation by parts, which is used for summing products of sequences.
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Description
Test your understanding of integration by parts with this quiz. Assess your ability to find the integral of a product of functions and transform the antiderivative of a product of functions into a more easily solvable form.
