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When determined integrals ∫ab f (x) dx become too difficult (almost all in practice) to determine exactly, remains numerical integration. We will look at the simplest, namely the rectangle formula. Divide the integration interval [a, b] for simplicity n equal length h = (b-a) / n, giving rise to a so called partition of the interval a = x0"<"x1 ... "<"xn" = b i n smaller intervals with the length h. The idea is now to approximate the integral with all the rectangles that are formed; with the base h and the height calculated in the middle of the current small range, see formula. Calculate some integrals this way.

So not using any of Mathematicas own integral tools. It should be as a Plot with the rectangles integrals under the line aswell as the calculations. Im really stuck on this and could really use some help. I don't even know where to start. The formulas are in a picture.

Formulas

Example of one integral

Hope someone can help me I have tried to search around but can't find anything that could help me.

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