Stewart_Calc_7ET ch08sec01
MULTIPLE CHOICE
1. Find the length of the curve.
a.
b.
c.
d.
e.
2. Find the length of the curve.
a.
b.
c.
d.
e.
None of these
3. Find the length of the curve for the interval .
a.
b.
c.
d.
e.
4. Find the length of the curve.
a.
13.05
b.
25.05
c.
d.
36.05
e.
None of these
5. Use Simpson’s Rule with n = 6 to estimate the length of the curve , .
Round your answer to six decimal places.
a.
6.987208
b.
6.947368
c.
6.972089
d.
6.947582
e.
None of these
6. Find the arc length of the graph from A to B.
a.
)
b.
)
c.
)
(1, 6)
(4, 20)
A
B
y = x3/2 + 42
1 2 3 4 5 x
2
4
6
8
10
12
14
16
18
20
22
24 y
80 10
80 10
80 10
d.
)
7. Find the arc length of the graph of the given equation on the specified interval.
y = ( + 1) , [2, 5]
a.
b.
c.
d.
8. Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer
to four decimal places.
P (3, 12), Q (3.2, 13.24)
a.
6.0828
b.
3.6497
c.
1.2166
d.
2.4331
9. Find the arc length function for the curve with starting point .
a.
b.
c.
80 10
81
243
2
81
2
243
4
d.
e.
10. Find the length of the line segment joining the two given points by finding the equation of the line
using Equation (2). Then check your answer by using the distance formula.
(0, 0), (1, 8)
a.
b.
9
c.
d.
11. Set up, but do not evaluate, an integral for the length of the curve.
a.
b.
c.
d.
e.
1. Set up, but do not evaluate, an integral that represents the length of the curve.
62
65
3
2. Find the length of the curve for the interval .
3. Set up, but do not evaluate, an integral for the length of the curve.
4. A hawk flying at an altitude of m accidentally drops its prey. The parabolic trajectory of the
falling prey is described by the equation
until it hits the ground, where y is its height above the ground and x is the horizontal distance traveled
in meters.
True or False?
The distance traveled by the prey from the time it is dropped until the time it hits the ground is
approximately m.
5. Set up, but do not evaluate, an integral for the length of the curve.
6. Use the arc length formula to find the length of the curve.
7. A steady wind blows a kite due west. The kite’s height above ground from horizontal position
to ft is given by
.
Find the distance traveled by the kite.
Give your answer rounded to two decimal places.
SHORT ANSWER
1. Find the arc length of the graph of the given equation from P to Q.
y = – 3x + 2; P (3, –7), Q (6, –16)
2. For the following exercise, (a) plot the graph of the function f, (b) write an integral giving the arc
length of the graph of the function over the indicated interval, and (c) find the arc length of the curve
accurate to two decimal places.
= x – ; [0, 6]
3. Write an integral giving the arc length of the graph of the equation from P to Q.
y = ; P (–2, ), Q (5, )
4. For the following exercise, (a) plot the graph of the function f, (b) write an integral giving the arc
length of the graph of the function over the indicated interval, and (c) find the arc length of the curve
accurate to two decimal places.
= x – 3 ; [0, 3]
1
13
1
34
y