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[ryanox]

the region under the curve y= (root) 2x/x (squared) +1 and bounded by the lines x=0 and x=1 is rotated about the x-axis. find the volume of the solid of revolution.

can neone do it??

 

[angels heap]

lines x=0 and 1, y=..., around x-axis: (i'll make { the interal sign..., and put between 1 and 0 in front)

around x-axis so V = {(y squared)dx

y squared = 2x/(x2 +1) -> squaring y removes the root over x

So V = pi (1,0){(y2) dx
= pi (1,0){ 2x/(x2 +1) dx -> integrate - it's a log so...
= pi [ln(x2 +1)](1,0) -> sub in (1,0) values
= pi [ln(2) - ln(1)] -> since ln1 = 0
= ln2pi units cubed

It's a little awkward because of the limited text availability, but hope that makes sense.

 

[ryanox]

thanks heaps angel heap