Chapter 7 Practice Test
1. Find the exact length of the curve
y=423x3/2-1
for
0x1
SOLUTION
dy/dx=42332x1/2=22 x1/2
L=011+(22 x1/2)2dx
=011+8x dx
= 2/31/8(1+8x)
= 13/6
3/2 from 0 to 1
2. Find the length of the curve y = x between (-8, -2) and (8, 2)
SOLUTION
dy/dx = ⅓x = 1/(3x )
L=-221+(3y2)2 dy
= 17.26
3. If f’(x) =½(x - 1/x ) find the length of the arc from ½ to 2
1/3
-⅔
2
2
Solution
4. If f(x) = 4x find the arc length from 0 to 1
SOLUTION
2
2/3
7.1
For #1 & 2
a. Determine when the particle is moving to the right, to the left and stopped.
b. Find the particles displacement for the given time interval. If s(0)=3, what is the particles final
position?
c. Find the total distance traveled by the particle.
1. v(t)= 5 cos t 0 ≤ 𝑡 ≤ 2𝜋
𝑡
2. 𝑣(𝑡) = 1+𝑡 2 0 ≤ 𝑡 ≤ 3
3. An automobile accelerates from rest at 1+1 + 3√𝑡 𝑚𝑝ℎ/𝑠𝑒𝑐 for 9 seconds.
a. What is its velocity after 9 seconds?
b. How far does it travel in those 9 seconds?
4. The rate of consumption of oil in the United States during the 1980’s (in billions of barrels per year) is
modeled by the function 𝐶 = 27.08 × 𝑒 𝑡/25 where t is the number of years after Jan. 1, 1980. Find the
total consumption of oil in the United States from January 1, 1980 to January 1, 1990.
Answers:
1.
2.
3.
4.
Find the volume of the solid generated by revolving the region bounded by the lines and curves
about the x-axis
1. 𝑦 = √9 − 𝑥 2 , 𝑦 = 0
Solution:
Find the volume of the solid generated by revolving the region about the y-axis
2. Region enclosed by 𝑥 = √5𝑦 2 , 𝑥 = 0, 𝑦 = −1, 𝑦 = 1
Solution: