What are the concepts of infinitesimal and integral?

The basic idea of infinitesimal method is limit thought-set a tiny element and discuss its limit situation of approaching zero; This is the same as calculus. By the way, Newton made this thing to solve physical problems.

In college physics, in many cases, using calculus to solve problems can be regarded as "differential element method". Compared with the infinitesimal method used in middle school physics competitions, it can be considered that its expression is more rigorous and formal, but its essence is still the same.

Calculus can do any problem that can be done by infinite square method. Of course, it may be more troublesome.

Sometimes calculus is not a differential method, such as directly giving the function of displacement versus time and finding the function of velocity versus time. At this time, calculus can be used directly without setting infinitesimal elements (velocity is defined as the derivative function of displacement against time).

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The infinitesimal method can be replaced by calculus, and the infinitesimal method used in the competition is no exception, as mentioned above. In fact, there is generally not much calculus (mainly basic ideas) for competitions. Some problems can be solved by infinitesimal methods, and it is more troublesome and error-prone to express them by calculus. Of course, it is better to master calculus skillfully.