Dive into the captivating realm of calculus with these comprehensive study notes for Calculus 5.4 S1, delving deep into the art of calculating the length of plane curves. Unveil the magic behind measuring the intricate paths that curves trace, and equip yourself with the tools to conquer the challe...
Con&a der pane cve y= T(X) /e an
nt aralTa,a. Cnbñunus on [a, 4] ohen
hal y= f(x) a
smo,th cuve
Gn a, 7 Ohal a Smasdh fun01 n
J = d(x) S moo&h h i anl-eval
Ca,A7 ohen h aeengh Lqe Jhis cve
ores a,] defaned a
L
P2oo
P
Sub sntavalsb ansaing P
Jpon
JPons , g Xn- bd
nd hal
b y
Q= o and = %, eb
e R, , e h
poans
a-. 1 n and yosn
hse pons thssiaiy h
äte egmenls. Jhese Qsrs eey mens fo am a
p gonal
hal we tan y d a» an aepxo xamalsn
pa
s 9ha Ce 9=f(1). ee
Kek e
etyh
SoNe egmen
, Jhen JJ
By M.UT
By (4)-{(%) )hu ¢/8
4 ) -(%) = 4 )
F
=am
max > 0 =
+ttn) d
No
1)
J d
Foga uve e zpused an sh
foam =JU)
@n Te,d), gh a dength
m y=C y+do 4c
d
y
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