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  "body": "\n## Summary\n\nA reduction formula expresses an integral that depends on an integer $n$ through the same integral with a smaller $n$. Repeated use of the formula reduces the integral to a simple case. [[Integration by parts|08Y1BBQTK9]] usually produces the formula.\n\n## Remarks\n\nFor $I_n = \\int_0^{\\pi/2} \\sin^n x \\, dx$, integration by parts gives $I_n = \\frac{n - 1}{n} I_{n-2}$ for $n \\ge 2$.\nWith $I_0 = \\pi/2$ and $I_1 = 1$, this gives all $I_n$.\nThese integrals lead to the [[Wallis product|0XCYA4YERS]].\n\n## Explanations\n\n### L1 human\n\nA reduction formula is a recursion for a family of integrals.\nEach step lowers a power, until the integral is easy.\n",
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