| Exam Board | Edexcel |
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| Module | C12 (Core Mathematics 1 & 2) |
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| Year | 2017 |
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| Session | June |
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| Topic | Indefinite & Definite Integrals |
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8. (a) Find \(\int \left( 3 x ^ { 2 } + 4 x - 15 \right) \mathrm { d } x\), simplifying each term.
Given that \(b\) is a constant and
$$\int _ { b } ^ { 4 } \left( 3 x ^ { 2 } + 4 x - 15 \right) \mathrm { d } x = 36$$
(b) show that \(b ^ { 3 } + 2 b ^ { 2 } - 15 b = 0\)
(c) Hence find the possible values of \(b\).