please-I-am-confiouse-1-and-2-1-x-dx-2-with-F-x-f-x-f-x-dx-

Question Number 130255 by stelor last updated on 23/Jan/21

please \dots . I am confiouse \dots . 1 and 2 .

1 . \int ∣ x ∣ d x = ? ?

2 . with {(F (x))}^{^{'}} = f (x) \int ∣ f (x) ∣ d x = ? ?

Answered by Olaf last updated on 23/Jan/21

\int ∣ x ∣ d x = {\begin{cases} - \frac{1}{2} x^{2} + C, x ⩽ 0 \\ + \frac{1}{2} x^{2} + C, x ⩾ 0 \end{cases}

\Rightarrow \int ∣ x ∣ d x = \frac{1}{2} x ∣ x ∣ + C

\int ∣ f (x) ∣ d x = {\begin{cases} - F (x) + C, f (x) ⩽ 0 \\ + F (x) + C, f (x) ⩾ 0 \end{cases}

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