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2 answers:
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Answer
,
,
Step-by-step explanation:
Given that
For the term .
Limits for is from
to
and for
is from
to
and the region
, for this double integration is the shaded region as shown in graph 1.
Now, reverse the order of integration, first integrate with respect to then with respect to
. So, the limits of
become from
to
and limits of
become from
to
as shown in graph 2.
So, on reversing the order of integration, this double integration can be written as
Similarly, for the other term .
Limits for is from
to
and limits for
is from
to
and the region
, for this double integration is the shaded region as shown in graph 3.
Now, reverse the order of integration, first integrate with respect to then with respect to
. So, the limits of
become from
to
and limits of
become from
to
as shown in graph 4.
So, on reversing the order of integration, this double integration can be written as
Hence, from equations ,
and
, on reversing the order of integration, the required expression is
Now, compare the RHS of the equation with
We have,
and
.
