Worksheet 6.4 Arc Length - Calculus Maximus Page 5
ADVERTISEMENT
1
2
3
4
5Calculus Maximus
WS 6.4: Arc Length
8. (AP BC 2011B-4) The graph of the differentiable function
y
f x
with domain 0
x
10
is shown
in the figure at right. The area of the region enclosed between the graph of f and the x-axis for
0
x
5
is 10, and the area of the region enclosed between the graph of f and the x-axis for 5
x
10
x and
x
is 27. The arc length for the portion of the graph of f between
0
5
is 11, and the arc length
x =10
x
for the portion of the graph of f between
5
and
is 18. The function f has exactly two critical
x = 3
x = 8
points that are located at
and
.
.
(a) Find the average value of f on the interval 0
x
5
10
ò
(
)
( )
+ 2
3 f x
dx
(b) Evaluate
. Show the computations that lead to your answer.
0
x
ò
( )
( )
=
(c) Let g x
f t
dt
. On what intervals, if any, is the graph of g both concave up and decreasing?
5
Explain your reasoning.
æ
ö
æ
ö
x
x
( )
( )
= 2 f
÷ . The derivative of h is ¢ h x
= ¢ f
(d) The function h is defined by h x
ç
ç
÷ . Find the arc
è
ø
è
ø
2
2
( )
y = h x
x = 0
x = 20
length of the graph of
from
to
.
Page 5 of 5
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education