Let ƒ be an integrable function on [a,b]. Which of the following is not always true?

A) $\int _ { b } ^ { b } f ( x ) d x = 0$
B)ƒ is a continuous function on [a,b].
C) $\int _ { a } ^ { b } f ( x ) d x$ is a real number.
D) $\left| \int _ { a } ^ { b } f ( x ) d x \right| \geq 0$
E) $\int _ { a } ^ { b } f ( x ) d x = - \int _ { b } ^ { a } f ( x ) d x$

Question

Let ƒ be an integrable function on [a,b]. Which of the following is not always true?

A) $\int _ { b } ^ { b } f ( x ) d x = 0$
B)ƒ is a continuous function on [a,b].
C) $\int _ { a } ^ { b } f ( x ) d x$ is a real number.
D) $\left| \int _ { a } ^ { b } f ( x ) d x \right| \geq 0$
E) $\int _ { a } ^ { b } f ( x ) d x = - \int _ { b } ^ { a } f ( x ) d x$

Quizplus · Accepted Answer

Being integrable on [a,b] does not necessarily mean ƒ is continuous on [a,b]. A function can be integrable with discontinuities within the interval.

Let ƒ Be an Integrable Function on [A,b] ∫bbf(x)dx=0\int _ { b } ^ { b } f ( x ) d x = 0∫bb​f(x)dx=0

Let ƒ Be an Integrable Function on [A,b] $\int _ { b } ^ { b } f ( x ) d x = 0$