Final answer:
To calculate the mass of a one-dimensional object with a variable density function, one must integrate the density function over the object's length. Without specific values for the length and the density function, a numerical answer cannot be provided.
Step-by-step explanation:
To find the mass of a one-dimensional object like a pencil with variable density, we need to integrate the density function over the length of the object. In this case, the question suggests that the density changes along the length of the pencil, possibly in a function denoted as ρ(x), where ρ represents the density and x represents the position along the pencil.
The general formula to calculate mass is m = ∫ density × dV, where dV is a small element of volume. For a one-dimensional object, dV effectively becomes a small element of length, dx. Thus, the mass of the pencil is found by integrating the density function from the starting point to the end of the pencil (the length), which can be mathematically represented as:
m = ∫_{a}^{b} ρ(x) dx
where a and b are the start and end points of the pencil, respectively.
However, without an explicit form of the density function or the actual length of the pencil, we cannot provide a numerical answer. Assuming the function ρ(x) is provided and the length of the pencil is known, we would then perform the integral over that interval to find the mass of the pencil.