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
<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).
</span>
<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).
</span>
<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.
</span>
<span>I hope this helps! </span>
Hello!!
I believe the correct answer to your question is capuchon. These are cone shaped ceremonial hats worn durning Mardi Gras.
Hope I helped with a detailed description. Have a nice night!
~Brooke❤️
This one is easy.
<span>–8.6 = –4.1 + x
</span>
So, what you have to do is add 4.1 on both sides.
You do this because you want to get X alone. when you do,
-8.6+4.1=-4.5
X=-4.5
The answer is B
Answer:
3
Step-by-step explanation:
