A sufficient condition for a function ƒ on [a,b] to be integrable is

A)ƒ is non-negative.
B)ƒ is positive.
C)ƒ is bounded above.
D)ƒ is bounded below.
E)ƒ is continuous.

Question

A sufficient condition for a function ƒ on [a,b] to be integrable is
​
A)ƒ is non-negative.
B)ƒ is positive.
C)ƒ is bounded above.
D)ƒ is bounded below.
E)ƒ is continuous.

Quizplus · Accepted Answer

A function being continuous on a closed interval [a,b] is a sufficient condition for it to be integrable on that interval. This is because continuity on a closed interval implies that the function does not have any infinite discontinuities or jump discontinuities, which are common obstacles to integrability.

A Sufficient Condition for a Function ƒ on [A,b] to Be