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Rotating - Calculus Two for Biological Sciences - Exam, Exams of Calculus

This is the Exam of Calculus Two for Biological Sciences which includes Numerical Sum, Approximation, Midpoint Rule, Terms, Modeled, Type Equilibrium Points, Starting Population etc. Key important points are: Rotating, Integrate, Region, Free Response, Solid Obtained, Long Rod, Average Density, Volume, Curves, Multiple Choice

Typology: Exams

2012/2013

Uploaded on 02/18/2013

abhaya
abhaya 🇮🇳

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Name: ________________________ Class: ___________________ Date: __________ ID: A
Midterm 1: February 13, 2008
Free Response
y
= 4 -
x
y
=
x
- 2
1. Sketch the region enclosed by and . Decide whether to integrate with respect to
x
or
y
.
2 2
Find the area of the region.
= =
y
x
y
x
2. Find the volume of the solid obtained by rotating the region bounded by and about the line
= 0
y
.
(
x
) = 8
3. The linear density of a 15 m long rod is kg/m, where
x
is measured in meters from one end o
f
(3 +
x
)2
the rod. Find the average density of the rod.
4. Use the method of cylindrical shells to find the volume of a solid obtained by rotating the region bounded by
the given curves about the
y
axis.
= 3 -
y
x
x
,y= 0
2
Multiple Choice
I
dentify the choice that best completes the statement or answers the question.
_
___ 5. A spring has a natural length of 22 cm. If a force of 15 N is required to keep it stretched to a length of 32 cm,
how much work is required to stretch it from 22 cm to 40 cm? Force to pull spring is given by
-
F
(
x
) = k (
x
x
)
0
Select the correct answer.
a. 3.43 J
b. 1.93 J
c. 2.93 J
d. 3.93 J
e. 2.43 J
1
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Name: ________________________ Class: ___________________ Date: __________ ID: A

Midterm 1: February 13, 2008

Free Response

1. Sketch the region enclosed by y = 4 - x^2 and y = x^2 - 2. Decide whether to integrate with respect to x or y.

Find the area of the region.

2. Find the volume of the solid obtained by rotating the region bounded by y =^ x and y = x about the line

y = 0.

3. The linear density of a 15 m long rod is ( x ) = 8 kg/m, where x is measured in meters from one end of

(3 + x ) 2

the rod. Find the average density of the rod.

  1. Use the method of cylindrical shells to find the volume of a solid obtained by rotating the region bounded by the given curves about the y axis.

y = 3^ x - x^2 ,y= 0

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 5. A spring has a natural length of 22 cm. If a force of 15 N is required to keep it stretched to a length of 32 cm, how much work is required to stretch it from 22 cm to 40 cm? Force to pull spring is given by

F (^ x ) =^ k (^ x - x 0 )

Select the correct answer. a. 3.43 J b. 1.93 J c. 2.93 J d. 3.93 J e. 2.43 J