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Questions and Answers
How is the integration by parts formula related to the product rule of differentiation?
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?
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?
Who discovered integration by parts?
- Pierre-Simon Laplace
- Leonhard Euler
- Isaac Newton
- Brook Taylor (correct)
What is the discrete analogue for sequences called?
What is the discrete analogue for sequences called?
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What did Brook Taylor first publish in 1715?
What did Brook Taylor first publish in 1715?
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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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