integration and log functions!!!!! (1 Viewer)

[RHINO7]

Can someone please help me with these questions?

i) Find the exact volume of the solid formed when the curve y=1/ (square root of) x is rotated about the x-axis from x=1 and x=3.


ii) Find the area between the curve y=lnx, the y-axis and the lines y=2 and y=4, correct to 3 significant figures.


PLEASE!

 

[Bank$]

I cant do i) because i forgot the solid formula lol but here is my answer for ii)

y=lnx
change this to x equals by this identity "log(a)y = x can be arranged to a^x=y"
and then do DX/DY (yes dx/dy) and then sub in for limits 2 and 3.
(your dy/dx will be e^x)

 

[jb_nc]

(i) you need to square y because its around the x-axis so the equation becomes y^2 = 1/x which integrates to ln x from 1 to 3. Remeber the forumla is like V = pi [ y^2 dx]
So the answer is (pi)*ln 3 because ln 1 = 0.

 

[RHINO7]

Thanks