| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find curve equation from derivative (straightforward integration + point) |
| Difficulty | Moderate -0.3 This is a straightforward integration question requiring standard techniques (power rule and splitting fractions) followed by using an initial condition to find the constant. While it has multiple steps and requires algebraic manipulation (rewriting x^(-4) terms and simplifying), it's a routine C1/C2 exercise with no conceptual challenges beyond applying learned methods systematically. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx) |
The curve with equation $y = f(x)$ passes through the point $(1, 6)$. Given that
$$f'(x) = 3 + \frac{5x^2 + 2}{x^4}, \quad x > 0,$$
find $f(x)$ and simplify your answer. [7]
\hfill \mbox{\textit{Edexcel C1 Q8 [7]}}