From the course: Assembling Calculus
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Numerical integrals
From the course: Assembling Calculus
Numerical integrals
- [Instructor 1] We've now seen a technique to compute values for derivatives numerically. Similar techniques exist to break an integral up into little boxes and add them. Philosophically, that's what we're doing in general calculus anyway, adding of infinitesimal areas to get an overall sum. And of course, we've been simulating that with our blocks. - [Instructor 2] We could just break up the area under the curve into rectangles, each with a width of delta x and height calculated for each delta x step along the curve. To follow the curve a bit more closely, we can change each rectangle into a trapezoid constructed from each pair of adjacent points along the curve. Each of these trapezoids has an area equivalent to a rectangle delta XY, with its height determined by averaging those two points. We can see that using narrower trapezoids on the right gives a better approximation of the area than using big ones. Not…
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