Section 5.2 Homework
mathexpert121
sec_5.2_hw_assignment.pdf
6/10/16, 11:49 PMSec 5.2 HW Assignment
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Current Score : – / 113 Due : Tuesday, June 14 2016 12:00 AM CDT
1. –/1 pointsLarCalc9 5.2.001.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
2. –/1 pointsLarCalc9 5.2.004.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
Sec 5.2 HW Assignment (Homework)
ahmed alarbash MATH 21414, section 13539, Summer 1 2016 Instructor: Mahmoud Basharat
WebAssign
dx9 x
dx2 x − 2
6/10/16, 11:49 PMSec 5.2 HW Assignment
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3. –/1 pointsLarCalc9 5.2.006.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
4. –/1 pointsLarCalc9 5.2.008.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dx1 20 − 6x
dxx 3
3 − x4
6/10/16, 11:49 PMSec 5.2 HW Assignment
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5. –/1 pointsLarCalc9 5.2.009.MI.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
6. –/9 pointsLarCalc9 5.2.009.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral.
dx3x 2 + 2
x3 + 2x
dx6x 5 + 5
x6 + 5x
6/10/16, 11:49 PMSec 5.2 HW Assignment
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7. –/1 pointsLarCalc9 5.2.011.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
8. –/1 pointsLarCalc9 5.2.012.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dxx 2 − 94
x
dx x
20 − x2
6/10/16, 11:49 PMSec 5.2 HW Assignment
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9. –/1 pointsLarCalc9 5.2.013.MI.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
10.–/4 pointsLarCalc9 5.2.013.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral.
dxx 2 + 6x + 4
x3 + 9x2 + 12x + 3
dxx 2 + 12x + 1
x3 + 18x2 + 3x + 2
6/10/16, 11:49 PMSec 5.2 HW Assignment
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11.–/1 pointsLarCalc9 5.2.014.MI.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
12.–/17 pointsLarCalc9 5.2.014.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral.
dx x(x + 4)
3x3 + 18x2 − 9
dx x(x + 2)
x3 + 3x2 − 17
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13.–/1 pointsLarCalc9 5.2.016.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
14.–/1 pointsLarCalc9 5.2.020.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dx2x 2 + 5x − 5
x − 8
dxx 3 − 5x2 + 3x − 10
x2 + 2
6/10/16, 11:49 PMSec 5.2 HW Assignment
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15.–/1 pointsLarCalc9 5.2.023.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
16.–/1 pointsLarCalc9 5.2.024.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dx 1
x + 1
dx 1
x4/5 1 + x1/5
6/10/16, 11:49 PMSec 5.2 HW Assignment
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17.–/1 pointsLarCalc9 5.2.027.MI.
Find the indefinite integral by u-substitution. (Hint: Let u be the denominator of the integrand. Remember to use ln(|u|) where appropriate.)
+ C
18.–/12 pointsLarCalc9 5.2.027.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral by u-substitution.
dx 1
5 + 2x
dx 1
8 + 2x
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19.–/1 pointsLarCalc9 5.2.030.
Find the indefinite integral by u-substitution. (Hint: Let u be the denominator of the integrand. Remember to use ln(abs(v)) where appropriate.)
+ C
20.–/1 pointsLarCalc9 5.2.031.MI.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dx − 1
x3
x3
dθcot θ 3
6/10/16, 11:49 PMSec 5.2 HW Assignment
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21.–/9 pointsLarCalc9 5.2.031.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral.
22.–/1 pointsLarCalc9 5.2.033.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dθcot θ 2
dxcsc(8x)
6/10/16, 11:49 PMSec 5.2 HW Assignment
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23.–/1 pointsLarCalc9 5.2.034.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
24.–/1 pointsLarCalc9 5.2.038.
Find the indefinite integral. (Remember to use ln(|u|) where appropriate.)
+ C
dxsec x 9
dt2 (csc(t)) 2
cot(t)
6/10/16, 11:49 PMSec 5.2 HW Assignment
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25.–/1 pointsLarCalc9 5.2.041.
Solve the differential equation. (Remember to use ln(|u|) where appropriate.)
y =
26.–/1 pointsLarCalc9 5.2.042.MI.
Solve the differential equation, such that the equation passes through the given point ( (Remember to use ln(|u|) where appropriate.)
y =
= , (1, 6)dy dx
5 x
x, y).
= , (−1, 6)dy dx
x − 16 x
6/10/16, 11:49 PMSec 5.2 HW Assignment
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27.–/10 pointsLarCalc9 5.2.042.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Solve the differential equation.
= , (−1, 3)dy dx
x − 29 x
6/10/16, 11:49 PMSec 5.2 HW Assignment
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28.–/1 pointsLarCalc9 5.2.052.
A differential equation, a point, and a slope field are given. (Remember to use ln(|u|) where appropriate.)
Use integration to find the particular solution of the differential equation. y =
29.–/1 pointsLarCalc9 5.2.053.
Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.)
= sec(x), (0,1)dy dx
dx 6 4
5x + 10
6/10/16, 11:49 PMSec 5.2 HW Assignment
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30.–/1 pointsLarCalc9 5.2.058.
Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.)
31.–/1 pointsLarCalc9 5.2.060.MI.
Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.)
32.–/1 pointsLarCalc9 5.2.068.
Find F '(x).
F '(x) =
dx 5 x − 1
x + 10
(csc 2θ − cot 2θ)2 dθ 0.9
0.4
F(x) = dt3 tan(t) x
0
6/10/16, 11:49 PMSec 5.2 HW Assignment
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33.–/1 pointsLarCalc9 5.2.070.
Find F '(x).
F '(x) =
34.–/1 pointsLarCalc9 5.2.074.
Find the area of the given region. Use a graphing utility to verify your result. (Round your answer to two decimal places.)
F(x) = dt x5 1
t1
y = 8 x ln(x)
6/10/16, 11:49 PMSec 5.2 HW Assignment
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35.–/1 pointsLarCalc9 5.2.077.
Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify your result. (Round your answer to three decimal places.)
36.–/1 pointsLarCalc9 5.2.079.MI.
Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify your result. (Round your answer to three decimal places.)
37.–/3 pointsLarCalc9 5.2.081.MI.
Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral. Let n = 4 and round your answer to four decimal places. Use a graphing utility to verify your result.
using the Trapezoidal Rule
using Simpson's Rule
calculator approximation
y = , x = 1, x = 2, y = 0x 2 + 8
x
y = 4 sec , x = 0, x = 2, y = 0πx 6
dx 5 12
x1
6/10/16, 11:49 PMSec 5.2 HW Assignment
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38.–/3 pointsLarCalc9 5.2.083.MI.
Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral. Let n = 4 and round your answers to four decimal places. Use a graphing utility to verify your result.
using the Trapezoidal Rule
using Simpson's Rule
calculator approximation
39.–/1 pointsLarCalc9 5.2.089.
Find a value of x such that the following relation holds true.
x =
ln x dx 6
2
dt = dt x 3
t1
x 1 t1/144
6/10/16, 11:49 PMSec 5.2 HW Assignment
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40.–/1 pointsLarCalc9 5.2.097.
Find the average value of the function over the given interval.
41.–/2 pointsLarCalc9 5.2.101.MI.
A population of bacteria is changing at a rate based on the function given below, where t is time in days. The initial population (when t = 0) is 1100.
Write an equation that gives the population at any time t, and find the population when t = 4 days. (Round your answer to the nearest whole number.)
f(x) = , [2, 4] 8 x2
= dP dt
2900 1 + 0.25t
P(t) =
P(4) =
6/10/16, 11:49 PMSec 5.2 HW Assignment
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42.–/1 pointsLarCalc9 5.2.102.MI.
Find the time required for an object to cool from 280°F to 260°F by evaluating the following where t is time in minutes. (Round your answer to four decimal places.)
min
43.–/7 pointsLarCalc9 5.2.102.MI.SA.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the time required for an object to cool from 330°F to 210°F by evaluating the following where t is time in minutes.
44.–/1 pointsLarCalc9 5.2.104.
The rate of change in sales S is inversely proportional to time t (t > 1) measured in weeks. Find S as a function of t if sales after 2 and 4 weeks are 157 units and 279 units, respectively. S(t) =
45.–/3 pointsLarCalc9 5.2.109.
t = dT10 ln 2
280 1 T − 100260
t = dT10 ln 2
330 1 T − 100210
6/10/16, 11:49 PMSec 5.2 HW Assignment
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(a) Use a graphing utility to graph the following equation.
(b) Evaluate the integral to find y2 in terms of x. (Use C as your constant of integration.)
4x2 − y2 = 3
y2 = e−∫(1/x) dx
y2 =
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(c) Are the tangents to the graphs in parts (a) and (b) perpendicular at the points of intersection? Yes
No
