| Exam Board | Edexcel |
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | June |
| Topic | Indefinite & Definite Integrals |
7. (a) Show that \(\frac { ( 3 - \sqrt { } x ) ^ { 2 } } { \sqrt { } x }\) can be written as \(9 x ^ { - \frac { 1 } { 2 } } - 6 + x ^ { \frac { 1 } { 2 } }\).
Given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { ( 3 - \sqrt { } x ) ^ { 2 } } { \sqrt { } x } , x > 0\), and that \(y = \frac { 2 } { 3 }\) at \(x = 1\),
(b) find \(y\) in terms of \(x\).