Hey, I was just wondering if there was a way to prove the power rule for integration using the definition of a definite integral. And I don't mean using the proof for the differentiation power rule, I mean is it possible to derive [itex]\displaystyle\large\int_a^b x^c=\frac{b^{c+1}-a^{c+1}} {c+1}[/itex] using the formula [itex]\displaystyle\large\int_a^b f(x)=\lim\limits_{n\to\infty} \sum\limits_{i=1}^n f(x^*_i)\Delta x[/itex] ?(adsbygoogle = window.adsbygoogle || []).push({});

I tried substituting the values for [itex]f(x^*_i)[/itex] and [itex]\Delta x[/itex] without any success.

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# Proof of integration power rule

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