| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Indefinite & Definite Integrals |
| Type | Improper integral evaluation |
| Difficulty | Standard +0.3 This is a straightforward improper integral requiring students to recognize the standard power rule integration, apply limits correctly, and evaluate the limit as the upper bound approaches infinity. While it's a Further Maths topic (improper integrals), the technique is routine and the algebra is simple, making it slightly easier than average overall but still requiring proper understanding of limits at infinity. |
| Spec | 4.08c Improper integrals: infinite limits or discontinuous integrands |
In this question you must show detailed reasoning.
Show that $\int_5^{\infty} (x-1)^{-2} dx = 1$. [5]
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q2 [5]}}