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we are given:f :[a,b]-R, f is integrable and bdd below(f is greater

than t(i use t instead of delta) for all x belongs to [a,b] ), t is

greater than 0

claim: 1/f is integrable.

solution: f is integrable implies f is bdd - f is bdd above and below

implies 1/f is bdd below and above - 1/f is bdd-{1}

f is greater than t and t is greater than 0 for all x

- f is greater than 0 for all x. - 1/f can not be infinity for all x-

1/f is continuous.{2}

from {1} & {2} 1/f is a bdd continuous function .

hence 1/f is integrable.