Find the diameter of a circle if the radius is equal to 8?
1 answer:
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Direct computation:
Parameterize the top part of the circle by
with , and the line segment by
with . Then
Using the fundamental theorem of calculus:
The integral can be written as
If there happens to be a scalar function such that
, then
is conservative and the integral is path-independent, so we only need to worry about the value of
at the path's endpoints.
This requires
So we have
which means is indeed conservative. By the fundamental theorem, we have
The dashed line is because the sign is greater than to be a solid line it has to be equal to or greater than and to the shading means any point on there works for the equation easiest way to test where you should shade is by plugging into the equation the point (0,0)
