Math 152, Spring 2011, Review for Midterm 1, sections 1–3, 7–9
Your first midterm examination is likely to contain some prob
lems that do not resemble these review problems.
I. Applications of Integration
(13) Find the volumes of the solids obtained by rotating the indicated region
R
in the
xy
plane about the specified axis:
(1) Region:
R
is bounded by
y
= 1,
y
= ln
x
and
x
=
e
2
.
Axes: (
a
) the line
y
=

1;
(
b
) the line
x
=

2.
(2) Region:
R
consists of all points (
x, y
) with 0
≤
x
≤
π
and 0
≤
y
≤
sin
x
.
Axes: (2
a
) the line
y
=

2;
(2
b
) the line
x
=

1.
(3) Region:
R
is bounded by
x
=
y
(4

y
) and the
y
axis
Axis: the
y
axis.
(4) Write down the integral used to compute the work done against
gravity in building a granite pyramid 500 feet high with a square
base of side length 800 feet. Take the density of granite as 170 lbs
per cubic foot. Explain in detail how the integral is obtained.
(5) There is a point
x
0
in the interval [5
,
7] where the function
f
(
x
) = (
x
2

4)

1
/
2
takes on its average value over that interval.
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 Fall '08
 Madey
 Physics, 500 feet, Lima, 170 lbs, 800 feet

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