| Exam Board | Edexcel |
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| Module | C1 (Core Mathematics 1) |
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| Year | 2009 |
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| Session | January |
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| Topic | Indefinite & Definite Integrals |
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A curve has equation \(y = \mathrm { f } ( x )\) and passes through the point (4, 22).
Given that
$$\mathrm { f } ^ { \prime } ( x ) = 3 x ^ { 2 } - 3 x ^ { \frac { 1 } { 2 } } - 7 ,$$
use integration to find \(\mathrm { f } ( x )\), giving each term in its simplest form.