A2 help please

Can you help me please

question: the diagram shows the curve y = 6/(3x+1)^(1/2). The shaded region is bound by the curve and the lines
x=2 x=9 and y= 0

ii) the shaded region is rotated completely about the x- axis. Show that the volume of the solid produced can be written in the form of k(ln)2 where the exact value of the constant k is to be determined.

Could you show some working or say what you have tried?

So I used the formula (pi) (intergrate) y^2

so y^2= 36/(3x+1)

then intergration

= (pi)36(1/3) x (1/3x+1)

then simlplify

12(pi)/3x +1

this is is where I got to ( I think I made a mistake in the intergration but dunno where)

Indeed - do you know what $\displaystyle \int \dfrac{1}{x} dx$ is

Ln(x)

Ln(x)

Should it be 12(pi)ln(3x+1) ?

How do I simplify this ?

Can I make it into 12(pi) ln4 ?