I assume each path
is oriented positively/counterclockwise.
(a) Parameterize
by

with
. Then the line element is

and the integral reduces to

The integrand is symmetric about
, so

Substitute
and
. Then we get

(b) Parameterize
by

with
. Then

and

Integrate by parts with



(c) Parameterize
by

with
. Then

and

1.) 144
2.) 8
3.) 262.5
4.) 36
5.) 630
6.) 440
let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function. Check the picture below.
Answer:
0.6
Step-by-step explanation:
The x increases by 5, while y increases by 3
Lets use the method, which is
.
Keep in mind that x goes horizontally along the axis, while y goes vertically on the axis.
So plug the numbers in.
0.6
Hence, the constant proportionality is 0.6.