Math 191
Practice Prelim 1
Fall 2005
No calculators, notes or books allowed.
To improve the chance for partial credit and also generally ease the work of grading,
please:
•
write clearly and be well organized;
•
use the page backs for ungraded scrap work and for checking your answers;
•
box in
your answers; and
•
reduce your answers as much as possible.
None of the calculations are long
and
none of the answers are long.
1. Evaluate the following expressions:
a)
integraldisplay
sec
2
(
x
)
dx
b)
d
dt
integraldisplay
1
t
3
cos
4
(
x
)
dx
c)
integraldisplay
2

2
x
3
1 +
x
6
dx
2. Consider the region bounded on the left by the
y
axis and on the right by the
curves
y
= sin(
x
) and
y
= cos(
x
). Find the area of the region.
3. a) Express the area under the curve
y
= sin(
x
) between
x
= 0 and
x
=
π
6
as a
limit of Riemann sums. (Use uniform partitions and the right hand rule.)
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 Fall '07
 BERMAN
 Math, Riemann, Righthand rule, sin B sin, cos B sin

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