How to understand the idea to find sum with infinite many terms? How is idea related to definite Integral?

Question

amistre64 · Answer

an integration is the sum of a continuous function .... a summation notation is a discrete version.

If the integration converges, then the discrete, which is smaller by default, has to converge as well

amistre64 · Answer

or at least thats the way i learned it ...

amistre64 · Answer

$$\sum_{1}^{3}x^2=14$$
$$\int_{1}^{3}x^2~dx=8.666...$$
which has me wonderingif im remembering things a little off

ikram002p · Answer

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take this as an example now u knw that the integral of f(x) here is an expresses to the area under the curve...
now lets try to conclude this formula using what we know about the area assuming we do not know the integration ...
do u wanna to do it ?

ikram002p · Answer

we start by taking a rectangular areas under the curve to approximate total area... got it until now ??
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