Установить, является ли функция F(x) первообрвзной для функции f(x). F(x)=x^6/3 ; f(x)=2x^5. Created by ksesha234. algebra-ru

3 ; f(x)=2x^5...

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$F(x)= \frac{x^6}{3}\; \; \; \; f(x)=2x^5\\F`(x)=( \frac{x^6}{3})`= \frac{1}{3}*6x^5=2x^5=f(x)$

F `(x) = f(x) => F(x) - первообразная для функции f(x)

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sangers1959

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∫(2*x⁵)dx=2*x⁶/6=x⁶/3 ⇒
F(x) является первообразной для функции f(x).

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