Moderate -0.8 This is a straightforward integration by substitution question with clear guidance. The substitution is given, requiring only mechanical application: find du = 2dx so 4x-8 = 2(2x-5)+2 = 2u+2, then integrate (2u+2)u^7 which is routine polynomial integration. The algebra is simple and the method is standard textbook practice, making it easier than average.
Attempt new limits for \(u\) at any stage (expect 0,1)
M1
or re-substitute & use \((\frac{3}{2}, 3)\)
\(\frac{12}{7}\)
A1
5 marks
S.R. If M1 A0 A0 M1 A0, award S.R. B1 for answer \(\frac{68}{72}, \frac{34}{36}\) or \(\frac{17}{18}\)
ISW
Attempt to connect $dx$ and $du$ | M1 | but not just $dx = du$
For $du = 2 dx$ AEF correctly used | A1 | sight of $\frac{1}{2}(du)$ necessary
$\int u^3 + u^7 (du)$ | A1 | or $\int u^7(u+1)(du)$
Attempt new limits for $u$ at any stage (expect 0,1) | M1 | or re-substitute & use $(\frac{3}{2}, 3)$
$\frac{12}{7}$ | A1 | 5 marks | AG WWW |
S.R. If M1 A0 A0 M1 A0, award S.R. B1 for answer $\frac{68}{72}, \frac{34}{36}$ or $\frac{17}{18}$ | ISW |
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