Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / 17 / a / Solution

The original PDF places the $-1$ outside the square root. Use the substitution rule with $t=\sqrt{x}$, so $dx=2tdt$ and the endpoints become $2$ and $3$. Polynomial division givesHence the definite integral is