exercise:7624a01247: Difference between revisions
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Each of the propositions | |||
Each of the propositions [[guide:66c44a0b4c#theorem-2|proposition]], [[guide:66c44a0b4c#theorem-3|proposition]], [[guide:66c44a0b4c#theorem-4|proposition]], and [[guide:66c44a0b4c#theorem-5|proposition]] corresponds to one of the basic properties of the definite integral as they are enumerated in Theorems [[guide:239bf7acf2#theorem-1|theorem]] through [[guide:239bf7acf2#theorem-5|theorem]]. In general, the proof of each is obtained by checking the special case <math>a=b</math> separately and then using the formula | |||
and | |||
basic properties of the definite integral | |||
as they are enumerated in Theorems | |||
In general, the proof of each is obtained by | |||
checking the special case <math>a=b</math> | |||
separately and then using the formula | |||
<math display="block"> | <math display="block"> | ||
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together with the appropriate property | together with the appropriate property | ||
of the integral. | of the integral. | ||
<ul style{{=}}"list-style-type:lower-alpha"><li>Prove | |||
<li>Prove | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li>Prove | <li>Prove [[guide:66c44a0b4c#theorem-2|proposition]]</li> | ||
<li>Prove [[guide:66c44a0b4c#theorem-3|proposition]]</li> | |||
<li>Prove [[guide:66c44a0b4c#theorem-5|proposition]]</li> | |||
</ul> | </ul> | ||
Latest revision as of 14:28, 24 November 2024
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[/math]
Each of the propositions proposition, proposition, proposition, and proposition corresponds to one of the basic properties of the definite integral as they are enumerated in Theorems theorem through theorem. In general, the proof of each is obtained by checking the special case [math]a=b[/math] separately and then using the formula
[[math]]
M_a^b(f) = \frac1{b-a} \int_a^b f(x)\;dx,
\quad \mbox{for $a \lt b$}
,
[[/math]]
together with the appropriate property of the integral.
- Prove proposition
- Prove proposition
- Prove proposition