SPS SPS FM 2024 February — Question 3 5 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionFebruary
Marks5
TopicStandard Integrals and Reverse Chain Rule
TypeImproper integral to infinity
DifficultyModerate -0.8 This is a straightforward improper integral requiring only basic power rule integration and limit evaluation. The calculation is direct: integrate x^(-3/2) to get -2x^(-1/2), evaluate from 4 to infinity, obtaining 0 - (-2/2) = 1. While it involves an improper integral (a Further Maths topic), the execution is mechanical with no conceptual challenges or multi-step reasoning.
Spec4.08c Improper integrals: infinite limits or discontinuous integrands

3. Show that \(\int _ { 4 } ^ { \infty } x ^ { - \frac { 3 } { 2 } } d x = 1\) [0pt]

3. Show that $\int _ { 4 } ^ { \infty } x ^ { - \frac { 3 } { 2 } } d x = 1$\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2024 Q3 [5]}}