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Rectangle method

In mathematics, the rectangle method of integral calculus uses an approximation to a definite integral, made by finding the area of a series of rectangles.

Either the left or right corners, or top middle of the boxes lie on the graph of a function, with the bases run along the x-axis. The approximation is taken by adding up the areas (base multiplied by height, a function value) of the rectangles that fill the space between two desired x-values.

\int_a^b f(x)\,dx \approx \sum_{i=1}^{n} f(i'\Delta x)\Delta x \quad \mbox{ where } \Delta x = \frac{b-a}{n} \;,\;                   i' : \begin{cases} i-1 	& \mbox{if left approx.}\\ 			                    i-\frac{1}{2}	& \mbox{if midpoint approx.}\\                                             i    	& \mbox{if right approx.}	\end{cases}
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