Final answer:
The student's question concerns the calculation of the length of a curve using integration, but it lacks sufficient information for a complete answer. Moreover, the provided starting point does not match the curve described. Additional information is needed to calculate the actual length of the curve.
Step-by-step explanation:
The student's question is about finding the length of the curve y=ln(1-x^2) from a particular point, which in this case is (0,1/2). However, the question seems to have missing information, such as the end point of the curve for which the length is to be determined. Normally, to find the length of a curve represented by a function f(x) on an interval [a, b], you would use the formula for the arc length of a curve in the Cartesian plane:
L = ∫_a^b √(1 + (f'(x))^2) dx
However, without the full range for x, we cannot calculate a numerical result. Also, it is worth noting that the initial point given, (0,1/2), does not lie on the curve described by y=ln(1-x^2), as the natural logarithm of (1 - 0^2) is actually 0, not 1/2. This question seems to have either a typo or requires additional clarification.
With regards to the additional references provided, they seem to be related to subjects like physics and mathematics, specifically dealing with topics such as decay constants, half-life, and growth rates. However, these concepts do not directly relate to the student's question about the arc length of a curve. It is important to address the student's concern directly and provide guidance relevant to their question.