21N.1.SL.TZ0.2

METHOD 1

recognition that $y=\int \cos \left(x-\frac{\mathrm{\pi }}{4}\right)dx$                 (M1)

$y=\sin \left(x-\frac{\mathrm{\pi }}{4}\right)\left(+c\right)$                 (A1)

substitute both $x$ and $y$ values into their integrated expression including $c$                 (M1)

$2=\sin \frac{\mathrm{\pi }}{2}+c$

$c=1$

$y=\sin \left(x-\frac{\mathrm{\pi }}{4}\right)+1$                 A1

 

METHOD 2

$\underset{2}{\overset{y}{\int }}dy=\underset{\frac{{\displaystyle 3\mathrm{\pi }}}{4}}{\overset{x}{\int }}\cos \left(x-\frac{\mathrm{\pi }}{4}\right)dx$                 (M1)(A1)

$y-2=\sin \left(x-\frac{\mathrm{\pi }}{4}\right)-\sin \frac{\mathrm{\pi }}{2}$                 A1

$y=\sin \left(x-\frac{\mathrm{\pi }}{4}\right)+1$                 A1

 

[4 marks]

[N/A]