(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to know if its possible to count undefined and defined integral from definition. When I have derivative of function, ex. [tex]x^3[/tex], I can count this from this: [tex]\left(x^n\right)^{\prime}=nx^{n-1}[/tex], but can also use definition

[tex]\lim_{h\to0}\frac{\left(x+h\right)^3-x^3}{h}[/tex] and its the same. But when I have integral, ex. [tex]\int x^3\mbox{d}x[/tex], I dont have any definition to count this, I must use [tex]\int x^n\mbox{d}x=\frac{x^{n+1}}{n+1}[/tex]. What can I do, if I didnt know this formule? is there any definition to count undefined integral, or I can use only formules based on assumption that we know what function has this derivative?

3. The attempt at a solution

Trying to do something with derivative definition, but it didnt help me. Thanks for answer;]

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# Homework Help: Integrals from definition

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