N26112A GCE Further Pure Maths 6675 June 2007.indd - Edexcel

7.
y
C
Leave
blank
R
O
4 x
Figure 1
Figure 1 shows part of the curve C with equation
y = arsinh x , x
0 .
(a) Find the gradient of C at the point where x = 4.
(3)
The region R, shown shaded in Figure 1, is bounded by C, the x-axis and the line x = 4.
(b) Using the substitution x = sinh 2 θ, or otherwise, show that the area of R is
where k is a constant to be found.
k1n 2+ 5 − 5,
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(10)
16
*N26112A01624*