exercise:B9900bab39: Difference between revisions
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Let <math>f</math> be a continuous function. | Let <math>f</math> be a continuous function. | ||
Using areas, show that | Using areas, show that | ||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li> | ||
If <math>f</math> is an odd function, then | If <math>f</math> is an odd function, then | ||
<math>\int_{-a}^a f(x) \; dx = 0</math>.</li> | <math>\int_{-a}^a f(x) \; dx = 0</math>.</li> | ||
<li> | <li> | ||
If <math>f</math> is an even function, then | If <math>f</math> is an even function, then | ||
<math>\int_{-a}^a f(x) \; dx = 2 \int_0^a f(x) \; dx</math>.</li> | <math>\int_{-a}^a f(x) \; dx = 2 \int_0^a f(x) \; dx</math>.</li> | ||
</ul> | </ul> | ||
Latest revision as of 21:14, 23 November 2024
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[/math]
Let [math]f[/math] be a continuous function. Using areas, show that
- If [math]f[/math] is an odd function, then [math]\int_{-a}^a f(x) \; dx = 0[/math].
- If [math]f[/math] is an even function, then [math]\int_{-a}^a f(x) \; dx = 2 \int_0^a f(x) \; dx[/math].