OCR MEI Further Pure Core 2019 June — Question 6 4 marks

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2019
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration using inverse trig and hyperbolic functions
TypeImproper integral to infinity with inverse trig
DifficultyStandard +0.8 This is an improper integral requiring knowledge of the inverse tan standard integral, proper limit notation, and evaluation at infinity. While the integration itself is standard (arctan formula), the improper integral aspect and need for rigorous limit handling elevates it above routine A-level questions. It's a solid Further Maths question but not exceptionally difficult—competent students should recognize the form and execute correctly.
Spec4.08c Improper integrals: infinite limits or discontinuous integrands

6 In this question you must show detailed reasoning.
Find \(\int _ { 2 } ^ { \infty } \frac { 1 } { 4 + x ^ { 2 } } \mathrm {~d} x\).

Question 6:
AnswerMarks
6DR
 1 1 x
I  dx arctan
 
2 4x2 2 2
2
as x → , arctan ½ x → ½ π
1
I  
AnswerMarks
8B1
B2
B1
AnswerMarks
[4]1.1b
2.4,2.2a
AnswerMarks
1.1b1 x
arctan
 
2 2
if ½ π only B1
AnswerMarks
0.393 or better(soi)
allow B1 if unsupported
Question 6:
6 | DR

 1 1 x
I  dx arctan
 
2 4x2 2 2
2
as x → , arctan ½ x → ½ π
1
I  
8 | B1
B2
B1
[4] | 1.1b
2.4,2.2a
1.1b | 1 x
arctan
 
2 2
if ½ π only B1
0.393 or better | (soi)
allow B1 if unsupported
6 In this question you must show detailed reasoning.\\
Find $\int _ { 2 } ^ { \infty } \frac { 1 } { 4 + x ^ { 2 } } \mathrm {~d} x$.

\hfill \mbox{\textit{OCR MEI Further Pure Core 2019 Q6 [4]}}