CALCULUS
posted by Anon
The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1))
A. Find the area of region R.
B. Find the volume of the solid formed when the region R is revolved about the xaxis.
C. The solid formed in part B is divided into two solids of equal volume by a plane perpendicular to the
xaxis. Find the xvalue where this plane intersects the xaxis.
Please show your work!

Steve
A.
∫[0,3] 1/√(x+1) dx
= 2√(x+1) [0,3]
= 2
B. using discs, v=∫πy^2 dx
= π∫[0,3] 1/(x+1) dx
= πlog(x+1) [0,3]
= πlog4
C. We want c where
π∫[0,c] 1/(x+1) dx = π∫[c,3] 1/(x+1) dx
log(c+1)log(0+1) = log(3+1)log(c+1)
2log(c+1) = log(4)
log(c+1) = log(2) (and not because 4/2=2)
c = 1
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