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Lecture 18

MAT136H1 Lecture 18: Arc Length cont.Premium


Department
Mathematics
Course Code
MAT136H1
Professor
Anthony Lam
Lecture
18

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MAT136Lecture18ArcLengthcont.
ArcLength:
1.Findthearclengthof intheintervalny =l cosx| | 0, ][ 3
π
xL=
π/3
01 )+ (dx
dy 2d
 x=
π/3
01anx+t2d
 x=
π/3
0secx
2d
 ecx x=
π/3
0
sd
 n=l secx anx| + t|
π/3
0
 n n=l2
|
|+3|
|l1| + 0|
 n(2 )= l+3
2. , 1x=x
y4+1
4y2 y 2
yL=
2
11 [y ]+ 4
131
y32d[y]
dy
dx =8
4y32
4y3=2
1 3 1
y3
 y=
2
11 [y ]+ 4
161
y6− 2 2d
=
2
1
y
[y ]
4
161
y6+ 2 2d
 =y
2
1[y ]
2
131
y32d
 (y )dy =
2
12
13+1
y3
3. anx, [0, /3]y=t π
therefore πf(x)dl2
πtanx(dl)S=
π/3
0
2
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