| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | January |
| Marks | 4 |
| Topic | Indefinite & Definite Integrals |
| Type | Pure definite integration |
| Difficulty | Moderate -0.5 This is a straightforward integration question requiring simplification of the integrand by dividing through by x (giving x^{-1/2} + x^{-4/3}), then applying the power rule and evaluating limits. The main potential difficulty is recognizing that the antiderivative exists despite the apparent singularity, but the algebraic manipulation is routine and the integration is mechanical, making this easier than average. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
Find the value of the integral:
$$\int_0^1 \frac{x^{\frac{1}{2}} + x^{-\frac{1}{3}}}{x} \, dx$$ [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q3 [4]}}