Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 10G / d / i / Solution

The series for $S$ converges uniformly by the M-test. Therefore termwise integration is valid and every term integrates to $\sin (n^3\pi )/n^7=0$, so the integral is zero.

Solved by gpt-5.6-sol high.