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 consider the domain of ln(x) and any potential issues that could arise.
The natural logarithm function ln(x) is defined for positive values of x, meaning that x must be greater than zero. Therefore, the interval for which ln(x) is defined is (0, ∞) or "x is greater than zero".
To determine if ln(x) is integrable on this interval, we need to check if there are any additional issues that could affect the integral.
In this case, ln(x) is a continuous function on its domain, meaning it does not have any vertical asymptotes or discontinuities within the interval (0, ∞). This ensures that the function is well-behaved and integrable.
Hence, the interval on which f(x) = ln(x) is integrable is (0, ∞), which is option (a).