## Most recent change of Integration

Edit made on November 04, 2008 by GuestEditor at 09:45:52

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Like differentiation, integration is part of calculus.

Integration is the inverse of differentiation, and it is needed to solve differential equations.

Integrating a curve (or line) between two limits (say, EQN:x={\alpha} and EQN:x={\beta} ) will give the area enclosed by the curve (or line), the x-axis and the lines EQN:x={\alpha} and EQN:x={\beta}. If a curve (or line) exists both above and below the x-axis between the limits a and b, the regions above and below the x-axis must be integrated separately and then summed to find the magnitude of the area.
Integrating a curve (or line) EQN:y=f(x) with respect to EQN:x between two limits (say, EQN:x={\alpha} and EQN:x={\beta} ) will give the area enclosed by the curve (or line), the x-axis and the lines EQN:x={\alpha} and EQN:x={\beta}. If a curve (or line) exists both above and below the x-axis between the limits EQN:{\alpha} and EQN:{\beta}, the regions above and below the x-axis must be integrated separately and then summed to find the magnitude of the area.

The general rule for integration of power functions is shown below:

* EQN:\int{ax^n}dx=\frac{ax^{n+1}}{n+1}+c

Or with limits:

* EQN:\int_{\alpha}^{\beta}ax^ndx=[\frac{a{\beta}^{n+1}}{n+1}]-[\frac{a{\alpha}^{n+1}}{n+1}]