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Volume question

There's a curve with equation y=1+1/2x^1/2 (y= 1 + 1 over 2 root x)

The shaded region R is bounded by the curve, the x axis and the lines x=1 and x=4, is rotated through 360 degrees about the x-axis. Using integration, show that the volume of the solid generated is

pi(5+0.5ln2)





I have got to volume = pi (integral of (1+1/2x^-1/2)^2) between 4 and 1 as the limits.


Thanks!
Reply 1
Avatar for Chewwy
Chewwy
17
y^2 = 1 + x^-1/2 + 1/4x

pi INT y^2 dx = pi[x + 2rtx + (1/4)lnx]

limits 1 and 4...

volume = pi[(4+4 + (1/2)ln2)-(1+2-0) = pi(5+0.5ln2)

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