What are the major benefits of the method of the reduction formula?? Aside from the fact that it is fast.
Does it really have any advantages over integration by parts and other forms of integration in terms of accuracy?
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Most reduction formulas are actually just derived from integration by parts, so it just saves you time doing it manually and if the answers are both explicit then the accuracy is the same. In fact, using a reduction formula you are probably less likely to make a mistake by not carrying a minus sign etc.
Henry Lee
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They don't have any accuracy benefits, but when you would normally need to integrate by parts several times a reduction formula can save you that time. Additionally, most reduction formulas are found through integration by parts, so in some sense if you redo that integration by parts when you don't need to you are doing unnecessary work.
DMcMor
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