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Forums
Mathematics
Calculus
The Basic Area Problem (introduction to the topic of integrals)
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[QUOTE="mcastillo356, post: 6848961, member: 506793"] Hi PF, I will try to give an example: ##y=2+\cos x##. The plot is a decreasing function in the interval ##[a,b]=[0,\pi]##. Let's make a partition of this interval. The points would have a shape like ##a=x_0=0<x_1<x_2<x_3\cdots<x_{n-1}<\pi=x_n=b##. Let's see what happens: no matter how big is ##n##, I could make ##\{x_0,x_1,x_2,\cdots,x_{n-1}\}## points to be in a very short interval; say for example ##[0,\frac{\pi}{2}]##. But the way to avoid this is to make the biggest interval to tend to ##0##. This way we ensure to have points all the way long ##[a,b]##. PD: this is not mine; I wouldn't have done without some guy's advice. Greetings! [/QUOTE]
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Forums
Mathematics
Calculus
The Basic Area Problem (introduction to the topic of integrals)
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