Question

the region in the first quadrant enclosed by the curves y=0 x=2 x=5 and y=1/root(1+x) is rotated about the x axis. the volume of the solid generated is:

a. pie In(5)
b.pie In(3/4)
c.pie In(4/3)
d.pie In(10)
e. pie In(2)

Answer 1

looks like you want
∫ 1/√(x+1) dx from 0 to 2
= ∫ (x+1)^(-1/2) dx from 0 to 2
= [ 2(x+1)^(1/2) ] from 0 to 2
= [2√(x+1) ] from 0 to 2
= 2√3 - 2√1
= 2√3 - 2

Answer 2

sorry, I found the area by mistake, you wanted the volume

vol = ∫ π y^2 dx from 0 to 2
= π ∫ 1/(x+1) dx from 0 to 2
= π [ ln(x1) ] from 0 to 2
= π(ln3 - ln1]
= π ln3