1.75: Power integration and solving for a limit

0606/13/O/N/17 — Question 5 · 5 marks

(i)
Find (7x10)35dx\displaystyle\int (7x - 10)^{-\frac{3}{5}}\,\mathrm{d}x.
[2]
(ii)
Given that 6a(7x10)35dx=2514\displaystyle\int_{6}^{a} (7x - 10)^{-\frac{3}{5}}\,\mathrm{d}x = \frac{25}{14}, find the exact value of aa.
[3]