Integration

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) $y=f(x)$ with respect to $x$ between two limits (say, $x={\alpha}$ and $x={\beta}$ ) will give the area enclosed by the curve (or line), the x-axis and the lines $x={\alpha}$ and $x={\beta}.$ If a curve (or line) exists both above and below the x-axis between the limits ${\alpha}$ and ${\beta},$ 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:

$\int{ax^n}dx=\frac{ax^{n+1}}{n+1}+c$

Or with limits:

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

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