Considere uma função integrável f open parentheses x close parentheses. Seja F open parentheses x close parentheses uma primitiva da f open parentheses x close parentheses. Com relação à integral definida integral subscript 0 superscript 1 f left parenthesis x right parenthesis d x, é correto afirmar que:


a.

integral subscript 0 superscript 1 f left parenthesis x right parenthesis d x equals F left parenthesis 1 right parenthesis minus F left parenthesis 0 right parenthesis


b.

integral subscript 0 superscript 1 f left parenthesis x right parenthesis d x equals F left parenthesis 1 right parenthesis minus F left parenthesis 0 right parenthesis plus c


c.

integral subscript 0 superscript 1 f left parenthesis x right parenthesis d x equals f to the power of straight prime left parenthesis 1 right parenthesis minus f to the power of straight prime left parenthesis 0 right parenthesis


d.

integral subscript 0 superscript 1 f left parenthesis x right parenthesis d x equals F left parenthesis 1 right parenthesis plus c


e.

Nenhuma das demais alternativas está correta.

RESPOSTA A
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Seja f open parentheses x close parentheses greater or equal than 0 uma função contínua. Com respeito à integral L equals integral subscript 0 superscript 1 f left parenthesis x right parenthesis d x é correto afirmar que: a. L corresponde ao valor da área da região delimitada pela curvas: left curly bracket left parenthesis x comma f left parenthesis x right parenthesis right parenthesis colon x element of left square bracket 0 comma 1 right square bracket right curly bracket, space left curly bracket left parenthesis x comma 0 right parenthesis colon x element of straight real numbers right curly bracket comma left curly bracket left parenthesis 0 comma y right parenthesis colon y element of straight real numbers right curly bracket text e end text left curly bracket left parenthesis 1 comma y right parenthesis colon y element of straight real numbers right curly bracket b. L spacecorresponde ao valor do comprimento da curva left curly bracket left parenthesis x comma f left parenthesis x right parenthesis right parenthesis colon x element of left square bracket 0 comma 1 right square bracket right curly bracket c. L spacecorresponde ao valor da área da região delimitada pela curvas: left curly bracket left parenthesis x comma f left parenthesis x right parenthesis right parenthesis colon x element of left square bracket 0 comma 1 right square bracket right curly bracket, space left curly bracket left parenthesis x comma negative f left parenthesis x right parenthesis right parenthesis colon x element of left square bracket 0 comma 1 right square bracket right curly bracket comma left curly bracket left parenthesis 0 comma y right parenthesis colon y element of straight real numbers right curly bracket text e end text left curly bracket left parenthesis 1 comma y right parenthesis colon y element of straight real numbers right curly bracket. d. Nenhuma das demais alternativas está correta. e. L corresponde ao valor da diferença dos limites lim for x not stretchy rightwards arrow 1 of f left parenthesis x right parenthesis minus lim for x not stretchy rightwards arrow 0 of f left parenthesis x right parenthesis.RESPOSTA A
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