Standard +0.3 This is a straightforward application of the mean value formula requiring integration of 1/(1+4x²), which is a standard arctangent form. The integration is routine (arctan substitution with u=2x), and the calculation is direct with symmetric limits simplifying the work. Slightly easier than average due to the standard form and symmetric interval.
4 In this question you must show detailed reasoning.
Determine the mean value of \(\frac { 1 } { 1 + 4 x ^ { 2 } }\) between \(x = - 1\) and \(x = 1\). Give your answer to 3 significant
figures. figures.
Question 4:
4 | DR
1
1 1
m e a n = d x
1 − ( − 1 ) 1 + 4 x 2
− 1
1
1 1
= d x
8 14 + x 2
− 1
1 1
= 2 a r c t a n 2 x
8 − 1
1
= arctan20.554
2 | B1
M1
A1
A1
[4] | 1.1
1.1
1.1
1.1 | 2
1 1 1
or u=2x du
2 1+u2 2
−2
1 2
= a r c t a n u
4 − 2 | M1 for rearranging
denominator correctly
into appropriate form
or for karctan2x
4 In this question you must show detailed reasoning.\\
Determine the mean value of $\frac { 1 } { 1 + 4 x ^ { 2 } }$ between $x = - 1$ and $x = 1$. Give your answer to 3 significant\\
figures. figures.
\hfill \mbox{\textit{OCR MEI Further Pure Core 2021 Q4 [4]}}