| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 6 |
| Topic | Indefinite & Definite Integrals |
| Type | Find curve from gradient |
| Difficulty | Easy -1.2 This is a straightforward integration question requiring only the power rule for integration and using a given point to find the constant of integration. It's a standard textbook exercise with no problem-solving insight needed, making it easier than average but not trivial since it requires correct application of two techniques. |
| Spec | 1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums |
The gradient of a curve is given by $\frac{dy}{dx} = 2x^{-\frac{1}{2}}$, and the curve passes through the point $(4, 5)$. Find the equation of the curve. [6]
\hfill \mbox{\textit{SPS SPS SM 2022 Q5 [6]}}