The report stated that while the part (a) was satisfactorily handled by majority of
the candidates who attempted this question, the part (b) was poorly handled. They
reportedly displayed poor knowledge of integration by substitution. Majority of them could not obtain the new limits of integration. They were expected to
respond as follows:
I art (). = (2 + 3)7 + x-1 dy= 7(2 + 3)6(2) + (Zx-1)(1)- (x-1)(Z)
n p a , smce y x Zx-1' dx X (2X-1)^{2}
= 14(2x +3)6 + 1 2'Hence dY/ ]= 14'/9.
(Zx-1) dx x =-
In part (b), candidates were expected to use the substitution u = x + 2 to solve the
integration J12X-14 dx. They were to obtain the new limits by substituting the
(x+Z)^{4}
old limits (1 and 2) into the expression u = x+ 2. These limits were (3 and 4).
Furthermore, since u = x + 2, then x = u - 2 and dx = du