19N.1.AHL.TZ0.H_2

$\frac{1}{2}{\text{e}}^{2x}$ seen       (A1)

attempt at using limits in an integrated expression $\left({\left[\frac{1}{2}{\text{e}}^{2x}\right]}_0^{\text{ln}k}=\frac{1}{2}{\text{e}}^{2\text{ln}k}-\frac{1}{2}{\text{e}}^0\right)$        (M1)

$=\frac{1}{2}{\text{e}}^{\text{ln}{k}^2}-\frac{1}{2}{\text{e}}^0$       (A1)

Setting their equation $=12$       M1

Note: their equation must be an integrated expression with limits substituted.

$\frac{1}{2}{k}^2-\frac{1}{2}=12$       A1

$\left(k^2=25\Rightarrow \right)k=5$       A1

Note: Do not award final A1 for $k=\pm 5$.

[6 marks]

[N/A]