Determine the interval on which f(x) = ln(x) is integrable.
(0, ∞)
[0, ∞)
(−∞, 0) U (0, ∞)
All reals
To determine the interval on which f(x) = ln(x) is integrable, we need to consider the properties of the natural logarithm function.
The natural logarithm function ln(x) is defined for positive values of x. It is not defined for x ≤ 0. Therefore, the integrability of ln(x) depends on the interval on which x lies.
Given that ln(x) is only defined for positive values of x, we can conclude that the interval on which f(x) = ln(x) is integrable is (0, ∞).
So, the correct option is (0, ∞).
To verify this result, you can also check the integrability of ln(x) by using the properties of the natural logarithm and integration techniques.
since lnx is defined only for x > 0
it's integral can be defined only for x>0
You figure out which of the choices matches that, I love and prefer the good ol' way of expressing relationships like that.