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Massey - Worldwide Integral Calculus 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 0 / 14

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    Here are some sample questions from Worldwide Center of Math Integral Calculus 1/e by David B. Massey published by the Worldwide Center of Mathematics. Worldwide Center of Math Integral Calculus includes over 1200 assignable online homework problems with helpful links to the appropriate section of the eBook. The interactive eBook includes embedded full length video lectures by the author, interactive graphs, and video solutions for selected problems.

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1. 0/1 points  |  Previous Answers WWCMIntegralCalc1 1.3.503c.XP.Tut. My Notes
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Points
Submissions Used
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0/1
 
Evaluate the integral.
 
12x3
1 + x2
 dx
 
3x4+6x2
Incorrect: Your answer is incorrect. webMathematica generated answer key + C

Solution or Explanation
12x3
1 + x2
 dx
12x
x2 + 0x + 1  12x3 + 0x2 − 0x + 0
 − (12x3 + 0x2 + 12x)
−12x
    right double arrow implies
    
12x3
1 + x2
 = 12x + 
−12x
1 + x2

12x3
1 + x2
 dx
 = 
12x − 
12x
1 + x2
dx
 = 6x2 − 6 ln(x2 + 1) + C     
Note: x2 + 1 > 0
So absolute value is not needed.

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2. –/1 points WWCMIntegralCalc1 2.5.501e.XP.Tut. My Notes
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–/1
 
Evaluate the improper integral (if convergent). (If the quantity diverges, enter DIVERGES.)
∞
1
x
 − 
1
x + 3
dx
1

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3. –/6 points WWCMIntegralCalc1 3.5.503e.XP. My Notes
Question Part
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–/1 –/1 –/1 –/1 –/1 –/1
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–/6
 
Let
a > 0.
 Consider the volume obtained by revolving the graph of
y = e−ax
 about the x-axis on larger and larger intervals of the form [0, M]. Sketch a representative picture.


(a) Find the volume for a fixed a and M.
units3

(b) What happens as
M → ∞
 for fixed a > 0?
The volume approaches
units3.

What does this seem to imply?
    

(c) What happens as a → 0 for fixed M?
The volume approaches
units3.

What situation does this represent?
    

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4. –/3 points WWCMIntegralCalc1 3.10.501a.XP.Tut. My Notes
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1 2 3
–/1 –/1 –/1
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–/3
 
A tank filled with water is
h = 4
 feet deep,
l = 5
 feet long, and
w = 3
 feet wide. (Use
62.5 lb/ft3
 as the weight density of water.)
(a) Find the hydrostatic pressure P, in
lb/ft2,
 on the bottom of the tank.
P = lb/ft2

(b) Find the hydrostatic force F, in lb, on the bottom of the tank.
F = lb

(c) Find the hydrostatic force F, in lb, on one of the narrow sides of the tank.
F = lb

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5. –/2 points WWCMIntegralCalc1 4.5.501h.XP.Tut. My Notes
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–/2
 
Find the radius of convergence (R) and the interval of convergence (I) for the series. (If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation.)
∞
1
n
3n
 xn
n=1
R = 
I = 

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6. –/1 points WWCMIntegralCalc1 5.4.501h.XP.Tut. My Notes
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Determine if the series
∞(−1)n − 1e1/n
n = 1
 converges by the Alternating Series Test. If the Alternating Series Test fails, use another test to determine if the series converges or diverges.
    

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