Math 152
Workshop 6
Spring 2011
1. The region
R
is bounded below by the
x
axis, bounded on the left by the line
x
= 1, bounded
on the right by the line
x
= 2, and bounded above by the curve
y
=
5 +
x
x
2
+ 4
x
+ 3
.
(a) Sketch the region
R
and set up a definite integral that gives the area of
R
. Then calculate
the integral in two ways:
i. Approximately
using the
fnInt(
program in your calculator.
ii. Exactly
using the method of partial fractions.
iii. Check
that the two answers are “the same” (that is, find approximate values for
the result of the second method).
(b) The region
R
is rotated around the
x
axis to generate a solid body
B
. Sketch
B
and set
up a definite integral that gives the volume of
B
. Calculate the integral in two ways:
i. Approximately
using the
fnInt(
program in your calculator.
ii. Exactly
using the method of partial fractions (be careful how you set this up – there
are
four
undetermined coefficients in the partial fraction decomposition).
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 Spring '11
 SOSA
 Calculus, Derivative, dx

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