Let
be a bounded function on the rectangular region
over the
-plane. Divide the rectangular region
by the straight lines parallel to
-axis and
-axis and denote the partitioned small rectangles by
. We denote this partition by
.
Now for each
, take an arbitrary point
and consider the sum of small rectangular parallelpiped
. Let
Sum |
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NOTE Fix and conside the integration of
from
to
with respect to
. Then we have
SOLUTION
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We evaluate
by keeping
as a constant.
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Exercise5-1 |
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It is possible to evaluate
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SOLUTION
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Let
be a function defined on the closed bounded region
on
-plane. Let
be a rectangular region containing
. Now divide the rectangular region
by the straight lines parallel to
-axis and
-axis and denote the partitioned small rectangles by
.
1. Let be constants. Then
Understanding |
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If the region ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Linearity |
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Theorem5-2-1. is called linearity of double integral. |