Anthony Reverri
Section 27
Workshop Week 1
This week’s workshop asks us to sketch the region
R
defined by 1 ≤
x
≤ 2 and 0 ≤
y
≤ 1/
x
3
. Essentially we are asked to sketch the shaded area defined by the integral. Shown below is
this sketch.
Next we are asked to find the number at point
a
which divides the area above in half. To
find
a,
first we need to find the total area under the curve. This is done by solving the integral
above. The work is shown below:
=
= 
=
 (
=
Now that we know the total area is , we know that half the area is
and all we have to do
is find the point
a
that is defined on 1 ≤
x
≤ 2. To do this we need to set
a
as one of the
boundaries on the integral and set the new integral equal to
Doing this will allow us to solve for
a point
a
which splits the area in half. The work for the process described above is shown below.

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We get
a
to equal
,
however, we only want the positive answer because it satisfies the condition
that
a
is defined on 1 ≤
x
≤ 2. The reason we get a negative answer is because the graph also
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 Spring '08
 sc
 Calculus, Binary relation, Euclidean geometry

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