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Integration by Parts Quiz

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Questions and Answers

How is the integration by parts formula related to the product rule of differentiation?

It can be thought of as an integral version of the product rule of differentiation (correct)

It is the same as the product rule of differentiation

It is unrelated to the product rule of differentiation

It is the inverse of the product rule of differentiation

What is the integration by parts formula?

$igint udv = uv + igint vdu$

$igint udv = uv - igint vdu$ (correct)

$igint udv = rac{u}{v} - igint vdu$

$igint udv = uv - rac{u}{v}igint vdu$

Who discovered integration by parts?

Pierre-Simon Laplace

Leonhard Euler

Isaac Newton

Brook Taylor (correct)

What is the discrete analogue for sequences called?

<p>Summation by parts</p> Signup and view all the answers

What did Brook Taylor first publish in 1715?

<p>The idea of integration by parts</p> Signup and view all the answers

Study Notes

Integration by Parts

The integration by parts formula is closely related to the product rule of differentiation, as both formulas involve the derivative of a product of functions.
The integration by parts formula is: ∫udv = uv - ∫vdu, where u and v are functions of x.
This formula is used to integrate products of functions, especially when one of the functions can be easily integrated and the other can be easily differentiated.

History of Integration by Parts

The integration by parts formula is attributed to Brook Taylor, an English mathematician.

Discrete Analogue

The discrete analogue for sequences is called the summation by parts formula.

Brook Taylor's Contributions

Brook Taylor first published his work on calculus, "Methodus Incrementorum Directa et Inversa", in 1715, which included the integration by parts formula.

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Description

Test your understanding of integration by parts with this quiz. Explore the process of finding the integral of a product of functions and transforming antiderivatives for easier solutions. This quiz covers the application of the integration by parts rule, which is analogous to the product rule of differentiation.