| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 5 |
| Topic | Integration with Partial Fractions |
| Type | Improper integrals with discontinuity |
| Difficulty | Moderate -0.3 This is a straightforward improper integral requiring substitution of the infinity limit, integration using the power rule for fractional indices, and evaluation at the bounds. While it involves an improper integral (a Further Maths topic), the technique is mechanical with no conceptual subtlety—students simply apply standard rules and verify the given result. |
| Spec | 4.08c Improper integrals: infinite limits or discontinuous integrands |
In this question you must show detailed reasoning.
Show that
$$\int_5^{\infty} (x - 1)^{-\frac{3}{2}} dx = 1$$
[5]
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q3 [5]}}