A student evaluates ∫x4sinxdx by writing successive derivatives of x4 and successive antiderivatives of sinx in parallel columns, then combining the products with alternating signs. Which statement best explains why this process ends after a finite number of pairings?
(a) The derivatives of x4 eventually cycle back to x4, closing the process.
(b) The derivatives of x4 eventually become zero, so no further non-zero products are formed.
(c) The derivatives of sinx eventually become zero, eliminating new terms.
(d) Because there can be at most four pairings—the degree of x4—the tabular pattern itself stops even though the functions remain non-zero.