Determine the interval on which f(x) = ln(x) is integrable.
(0, �‡)
[0, �‡)
(−�‡, 0) U (0, �‡)(MY ANSWER)
All reals
I assume that ‡ means ∞
You know that ln(x) is only defined for x in (0,∞)
Your answer holds for f(x) = ln(|x|), not ln(x)
The correct interval on which the function f(x) = ln(x) is integrable is (0, ∞).
To determine the integrability of a function, we need to consider its properties and examine potential issues that could arise during integration. In this case, since the function is the natural logarithm of x, it is important to note that the natural logarithm is defined only for positive values of x.
Therefore, the interval (0, ∞) is the appropriate domain for the function where it is defined, and consequently, where it is integrable.
To determine the interval on which f(x) = ln(x) is integrable, we need to consider the domain of the function and check for any potential issues with the integrability.
The natural logarithm function, ln(x), is defined for positive real numbers, so its domain is (0, +∞). This means that the interval where f(x) = ln(x) is defined is (0, +∞).
To check for potential issues with integrability, we need to examine any points where the function may be discontinuous or have singularities. In the case of ln(x), the function is continuous and well-behaved on its defined domain with no singularities or discontinuities.
Therefore, the correct interval on which f(x) = ln(x) is integrable is (0, +∞).