i have some question about math 181

1. Consider the curves

y=2√x and y=x
and the region

R

bounded by both curves in the first quadrant.

(a) Find the area of

R
.

(b) Find the volume of the solid obtained by rotating

R
about the

x
-axis

2. Consider the region

S
in the first quadrant bounded by

y= cube root of x
and

y

=

8

. Find the volume of the solid obtained by rotating

S
about the

y

-axis.

3. Find the length of the curve

y= 2/3 x^(3/2)
on the interval

[3,8]

4. Consider the triangle with vertices

(

0

,

0

)

,

(2,0)
and

(

2

,

2

)

. Calculate the volume of the solid obtained by rotating this triangle about the line

y=

−

3

 

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