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Let f(x) > 0 for all real x. Then integral `int_a^b f(x) dx` is which of the...

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christinaeliz... | Honors

Posted August 9, 2012 at 2:09 AM via web

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Let f(x) > 0 for all real x. Then integral `int_a^b f(x) dx` is which of the following:

(A) is greater than zero if a > b.

(B) is always less or equal to zero.

(C) is always greater or equal than zero.

(D) is greater than zero when a < b .

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 9, 2012 at 2:44 AM (Answer #1)

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It is given that f(x) > 0 for all real x.

`int_(a)^b f(x) dx`

=> `f(b) - f(a)`

Both of f(b) and f(a) are greater than 0, but it is not known whether f(b) = f(a)

If b > a, the integral` int_(a)^b f(x) dx` is greater than or equal to 0.

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