Answer to question 1
The given line integral is
We evaluate the first line integral from
to
.
An equation of the straight line joining
and
in the xy plane is
.
The first line integral now becomes,
We evaluate the second line integral from
to
.
An equation of the straight line joining
and
in the xy plane is
.
The second line integral now becomes,
We now evaluate the third line integral from
to
.
An equation of the straight line joining
and
in the xy plane is
.
The third line integral now becomes,
We now evaluate the fourth line integral from
to
.
An equation of the straight line joining
and
in the xy plane is
.
The fourth line integral now becomes,
We now add all the line integrals to get,
Answer to question 2
According to the Green's Theorem,
.
This implies that,
This simplifies to
We evaluate the inner integral to get,
We now integrate again, to obtain,