Considere a função f left parenthesis x right parenthesis equals x e to the power of negative x end exponent. Com relação a integral imprópria integral subscript 0 superscript straight infinity f left parenthesis x right parenthesis d x, é correto afirmar que:

a. integral subscript 0 superscript straight infinity f left parenthesis x right parenthesis d x equals e to the power of negative 1 end exponent

b. integral subscript 0 superscript straight infinity f left parenthesis x right parenthesis d x equals e

c. integral subscript 0 superscript straight infinity f left parenthesis x right parenthesis d x text não é convergente. end text

d. integral subscript 0 superscript straight infinity f left parenthesis x right parenthesis d x equals 1

e. integral subscript 0 superscript straight infinity f left parenthesis x right parenthesis d x equals 0