MATH 101B (Calculus II)
TEST #2 (Chapter 6)
Name:
Total: 100 points
1.
Find the position and velocity of an object moving along a straight line with the
given acceleration, initial velocity, and initial position.
(10 points)
a(t) = 11e−t , v(0) = −11, and s(0) = 17 .
2.
Find the area of the region bounded by:
(10 points)
y = 7x , the line y = 2x − 7 , and y = 0 .
3.
Use the Disk Method to calculate the volume obtained by rotating the region
bounded by y = 25− x 2 , y = 0 , x = 0 , x = 3 about the x axis.
4.
(10 points)
Set up the problem to find the volume of the solid obtained by rotating the
region between the graphs of f (x) = x , and g(x) = x about the line x = 4 .
(8 points)
5.
Use the shell method to find the volume generated by rotating the region bounded
by y = x 2 , and x = y 2 about y = −5 .
(12 points)
6.
Find the arc length of the curve y = 2 x 2 on [0, 3]
7.
SET UP ONLY!
A water tank in the shape of an inverted cone has a height of 28m and a base
radius 7m, is filled with water to a depth of 16m. Determine the amount of work
needed to pump all of the water to the top of the tank. (Assume density of the
water is 1000 kg/ m 3 ).
(10 points.)
3
8.
Find
π
6
∫ (2
cos3t
sin 3t)dt
(10 points.)
(10 points.)
0
9.
SET UP ONLY!
The dam has a shape of a semicircle with the diameter 80 m. Assume the water
level is at the top of the dam. Find the total force on the face of the dam. (10 points)
10.
The homicide rate decreases at a rate of 6% per year in a city that has 800
homicides per year in 2003. At this rate, when will the homicide rate reach 500
homicides per year?
(10 points)