| Line 3: | Line 3: | ||
! style="background-color: rgb(228, 188, 126); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Table of Definite Integrals | ! style="background-color: rgb(228, 188, 126); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Table of Definite Integrals | ||
|- | |- | ||
| − | ! style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | | + | ! style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Definition of Definite Integral |
|- | |- | ||
|<math> \int\limits_{a}^{b} f ( x ) d x = \lim_{n \to \infty} { f ( a ) \Delta x + f ( a + \Delta x ) \Delta x + f ( a + 2 \Delta x ) + \cdot \cdot \cdot + f ( a + ( n - 1 ) \Delta x ) \Delta x }</math> | |<math> \int\limits_{a}^{b} f ( x ) d x = \lim_{n \to \infty} { f ( a ) \Delta x + f ( a + \Delta x ) \Delta x + f ( a + 2 \Delta x ) + \cdot \cdot \cdot + f ( a + ( n - 1 ) \Delta x ) \Delta x }</math> | ||
| Line 13: | Line 13: | ||
|<math> \int\limits_{-\infty}^{\infty} f ( x ) d x = \lim_{a \to - \infty \ b \to \infty} \int\limits_{a}^{b} f ( x ) d x</math> | |<math> \int\limits_{-\infty}^{\infty} f ( x ) d x = \lim_{a \to - \infty \ b \to \infty} \int\limits_{a}^{b} f ( x ) d x</math> | ||
|- | |- | ||
| − | |<math> \int\limits_{a}{b} | + | |<math> \int\limits_{a}^{b} f ( x ) d x = \lim_{\epsilon \to \infty} \int\limits_{a}^{b - \epsilon} f ( x ) d x</math> |
| + | |- | ||
| + | |<math> \int\limits_{a}^{b} f ( x ) d x = \lim_{\epsilon \to \infty} \int\limits_{a + \epsilon}^{b} f ( x ) d x</math> | ||
Revision as of 07:18, 15 November 2010
| Table of Definite Integrals | |
|---|---|
| Definition of Definite Integral | |
| $ \int\limits_{a}^{b} f ( x ) d x = \lim_{n \to \infty} { f ( a ) \Delta x + f ( a + \Delta x ) \Delta x + f ( a + 2 \Delta x ) + \cdot \cdot \cdot + f ( a + ( n - 1 ) \Delta x ) \Delta x } $ | |
| $ \int\limits_{a}^{b} f ( x ) d x = \int\limits_{a}^{b} \frac{d}{dx} g ( x ) d x = g ( x ) |_{a}^{b} = g ( b ) - g ( a ) $ | |
| $ \int\limits_{a}^{\infty} d x = \lim_{n \to \infty} \int\limits_{a}^{b} f ( x ) d x $ | |
| $ \int\limits_{-\infty}^{\infty} f ( x ) d x = \lim_{a \to - \infty \ b \to \infty} \int\limits_{a}^{b} f ( x ) d x $ | |
| $ \int\limits_{a}^{b} f ( x ) d x = \lim_{\epsilon \to \infty} \int\limits_{a}^{b - \epsilon} f ( x ) d x $ | |
| $ \int\limits_{a}^{b} f ( x ) d x = \lim_{\epsilon \to \infty} \int\limits_{a + \epsilon}^{b} f ( x ) d x $ | |
