b)
C
R
O
5
x > 0.
Figure 2 shows a sketch of part of the curve C with equation $y = \frac{5}{x\sqrt{(2x+1)}}$
The finite region R is bounded by the curve C, the x-axis, the line with equation $x = 1$
and the line with equation $x = 4$.
This region is shown shaded in Figure 2.
The region R is rotated through 360° about the x-axis.
Use calculus to find the exact volume of the solid of revolution generated, giving your
answer in the form $a + b \ln c$, where a, b and c are constants.
(6)
