| Exam Board | Edexcel |
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| Module | C12 (Core Mathematics 1 & 2) |
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| Year | 2014 |
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| Session | June |
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| Topic | Standard Integrals and Reverse Chain Rule |
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7. (i) A curve with equation \(y = \mathrm { f } ( x )\) passes through the point \(( 2,3 )\).
Given that
$$f ^ { \prime } ( x ) = \frac { 4 } { x ^ { 3 } } + 2 x - 1$$
find the value of \(\mathrm { f } ( 1 )\).
(ii) Given that
$$\int _ { 1 } ^ { 4 } ( 3 \sqrt { x } + A ) \mathrm { d } x = 21$$
find the exact value of the constant \(A\).