Math 2414 DHW 4
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School
University of Texas, Dallas *
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Course
2413
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by DoctorLightning3936
Ashwin Indurti
Math2414SP24
Assignment DHW
4
–
7.2
-
7.3
–
S24 due 02/12/2024 at 11:59pm CST
Problem 1.
(1 point)
Evaluate the integral.
Z
8sin
3
(
x
)
cos
5
(
x
)
dx
=
Answer(s) submitted:
•
-4/3cosˆ6(x)+cosˆ8(x)+c
(correct)
Correct Answers:
•
8*(-0.125*[sin(x)]ˆ2*[cos(x)]ˆ6-0.0416667*[cos(x)]ˆ6)+C+C
Problem 2.
(1 point)
Evaluate the integral.
Z
π
/
2
0
sin
5
x
cos
8
xdx
=
Answer(s) submitted:
•
8/1287
(correct)
Correct Answers:
•
1/(8+1)-2/(8+3)+1/(8+5)
Problem 3.
(1 point)
Evaluate the integral.
Z
-
9sin
5
(
x
)
dx
=
Answer(s) submitted:
•
-9(-cos(x)+((2cosˆ3(x))/3) - (cosˆ5(x))/5)+c
(correct)
Correct Answers:
•
1.8*[cos(x)]ˆ5+-6*[cos(x)]ˆ3-(-9)*cos(x)+C
Problem 4.
(1 point)
Evaluate the integral.
Z
-
9sin
6
(
x
)
cos
3
(
x
)
dx
=
Answer(s) submitted:
•
-9/7sinˆ7(x)+sinˆ9(x)+c
(correct)
Correct Answers:
•
-1.28571*[sin(x)]ˆ7--1*[sin(x)]ˆ9+C
Problem 5.
(1 point)
Evaluate the integral.
Z
9cos
4
xdx
=
Answer(s) submitted:
•
9(cosˆ3(x)sinx+3/8(x-1/4sin(4x)))+c
(correct)
Correct Answers:
•
2.25*[cos(x)]ˆ3*sin(x)+3.375*cos(x)*sin(x)+3.375*x+C
Problem 6.
(1 point)
Evaluate the integral.
Z
6sin
2
(
7
x
)
dx
=
.
Answer(s) submitted:
•
3(x-1/14sin(14x))+c
(correct)
Correct Answers:
•
6*x/2-0.214286*sin(14*x)+C
Problem 7.
(1 point)
Evaluate the integral.
Z
π
/
2
0
5sin
2
(
x
)
cos
2
(
x
)
dx
=
Answer(s) submitted:
•
(5pi)/16
(correct)
Correct Answers:
•
5*pi/16
Problem 8.
(1 point)
Evaluate the integral.
Z
π
/
4
0
4cos
2
(
θ
)
tan
2
(
θ
)
d
θ
=
Answer(s) submitted:
•
-1+pi/2
(correct)
Correct Answers:
•
4*(pi/8-1/4)
Problem 9.
(1 point)
Evaluate the integral.
Z
π
/
4
0
3sin
4
(
x
)
cos
2
(
x
)
dx
=
Answer(s) submitted:
•
-1/8+(9pi+12)/192
(correct)
Correct Answers:
•
3/192*(3*pi-4)
1
Problem 10.
(1 point)
Evaluate the integral.
Z
4tan
3
(
4
x
)
sec
5
(
4
x
)
dx
=
Answer(s) submitted:
•
4(((secˆ7(4x))/28)-(secˆ5(4x))/20)+c
(correct)
Correct Answers:
•
-0.2*[sec(4*x)]ˆ5+0.142857*[sec(4*x)]ˆ7+C
Problem 11.
(1 point)
Evaluate the integral.
Z
-
2cot
3
(
w
)
csc
3
(
w
)
dw
=
Answer(s) submitted:
•
((((1/5cscˆ5(w)-1/3(cscˆ3(w))))))2+c
(correct)
Correct Answers:
•
-0.666667*[csc(w)]ˆ3--0.4*[csc(w)]ˆ5+C
Problem 12.
(1 point)
Evaluate the integral.
Z
tan
4
(
x
)
sec
4
(
x
)
dx
=
Answer(s) submitted:
•
(tanˆ5(x))/5 + (tanˆ7(x))/7 + c
(correct)
Correct Answers:
•
1/5*[tan(x)]ˆ5+1/7*[tan(x)]ˆ7+C
Problem 13.
(1 point)
Evaluate the integral.
Z
-
7csc
4
(
x
)
cot
6
(
x
)
dx
=
Answer(s) submitted:
•
cotˆ7(x)+7/9cotˆ9(x)+C
(correct)
Correct Answers:
•
1*[cot(x)]ˆ7+0.777778*[cot(x)]ˆ9+C
Problem 14.
(1 point)
Evaluate the integral.
Z
-
10tan
3
(
x
)
cos
4
(
x
)
dx
=
Answer(s) submitted:
•
-10((tanˆ4(x)/4)+(tanˆ6(x)/6))+C
(correct)
Correct Answers:
•
-2.5*[tan(x)]ˆ4+-1.66667*[tan(x)]ˆ6+C
Problem 15.
(1 point)
Evaluate the integral.
Z
π
/
4
0
9sec
4
(
x
)
tan
4
(
x
)
dx
=
Answer(s) submitted:
•
108/35
(correct)
Correct Answers:
•
12*9/35
Problem 16.
(1 point)
Evaluate the integral.
Z
6tan
2
(
6
x
)
dx
=
Answer(s) submitted:
•
-6x+tan(6x)+c
(correct)
Correct Answers:
•
1*tan(6*x)-6*x+C
Problem 17.
(1 point)
Evaluate the integral.
Z
-
9tan
4
(
x
)
dx
=
Answer(s) submitted:
•
-9(1/3tanˆ3(x) + x - tan(x))+C
(correct)
Correct Answers:
•
-3*[tan(x)]ˆ3-(-9)*tan(x)+(-9)*x+C
Problem 18.
(1 point)
Evaluate the indefinite integral.
Z
sec
3
xdx
=
Answer(s) submitted:
•
1/2(sec(x)tan(x))+1/2ln|tan(x)+sec(x)|+C
(correct)
Correct Answers:
•
[sec(x)*tan(x)+ln(|sec(x)+tan(x)|)]/2+C
Problem 19.
(1 point)
Evaluate the integral.
Z
9tan
2
(
x
)
sec
(
x
)
dx
=
Answer(s) submitted:
•
9(1/2sec(x)tan(x)-1/2ln|tan(x)+sec(x)|)+c
(correct)
Correct Answers:
•
4.5*[sec(x)*tan(x)-ln(|sec(x)+tan(x)|)]+C
2
Problem 20.
(1 point)
Evaluate the integral.
Z
-
5
(
1
-
x
2
)
3
/
2
dx
=
Answer(s) submitted:
•
-5x/sqrt(1-xˆ2)+c
(correct)
Correct Answers:
•
-5*x/[(1-xˆ2)ˆ0.5]+C+C
Problem 21.
(1 point)
Evaluate the integral.
Z
√
2
/
2
0
9
x
2
√
1
-
x
2
dx
=
Answer(s) submitted:
•
99(pi-2)/88
(correct)
Correct Answers:
•
9*(pi/8-1/4)
Problem 22.
(1 point)
Evaluate the integral.
Z
2
/
3
0
-
7
x
3
p
4
-
9
x
2
dx
=
Answer(s) submitted:
•
(incorrect)
Correct Answers:
•
-7*64/1215
Problem 23.
(1 point)
Evaluate the integral.
Z
-
10
√
x
2
+
16
dx
=
Answer(s) submitted:
•
-10ln(1/4|x+sqrt(16+xˆ2)|)+c
(correct)
Correct Answers:
•
-10*ln(|x+sqrt(xˆ2+16)|)+C
Problem 24.
(1 point)
Evaluate the integral.
Z
2
0
5
x
3
p
x
2
+
4
dx
=
Answer(s) submitted:
•
(64sqrt2+64)/3
(correct)
Correct Answers:
•
64*5/15*[sqrt(2)+1]
Problem 25.
(1 point)
Use the substitution
x
=
2tan
(
θ
)
to evaluate the indefinite integral
Z
7
x
2
√
x
2
+
4
dx
=
Answer(s) submitted:
•
-7sqrt(4+xˆ2)/(4x)+c
(correct)
Correct Answers:
•
-[7/(4*x)]*sqrt(xˆ2+4)+C
Problem 26.
(1 point)
Evaluate the integral.
Z
5
x
3
√
x
2
-
25
dx
=
Answer(s) submitted:
•
5(1/3(xˆ2-25)ˆ(3/2)+25sqrt(xˆ2-25))+c
(correct)
Correct Answers:
•
125*sqrt(xˆ2-25)+1.66667*[sqrt(xˆ2-25)]ˆ3+C
Problem 27.
(1 point)
Evaluate the integral.
Z
-
2
√
x
2
-
9
x
3
dx
=
Answer(s) submitted:
•
sqrt(xˆ2-9)/(xˆ2)-1/3arcsec(x/3)+c
(correct)
Correct Answers:
•
-0.111111/(xˆ2)*(xˆ2-9)ˆ1.5--0.111111*(xˆ2-9)ˆ0.5--0.33333
Problem 28.
(1 point)
Evaluate the integral.
Z
2
√
2
-
8
t
3
√
t
2
-
1
dt
=
Answer(s) submitted:
•
-pi/3-sqrt3+2
(correct)
Correct Answers:
•
-8*(pi/24+[sqrt(3)]/8-1/4)
3
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Problem 29.
(1 point)
Evaluate the integral by completing the square and using trigono-
metric substitution.
Z
1
√
x
2
+
4
x
+
8
dx
=
Answer(s) submitted:
•
ln(1/2|x+2+sqrt(xˆ2+4x+8)|)+C
(correct)
Correct Answers:
•
ln(|sqrt((x+2)ˆ2+4)+x+2|)+C
Problem 30.
(1 point)
Evaluate the integral.
Z
4
x
2
√
4
x
-
x
2
dx
=
Answer(s) submitted:
•
4(6arcsin(1/2x-1)-sin(2arcsin(1/2x-1))-4sqrt(-xˆ2+4x))+c
(correct)
Correct Answers:
•
24*asin((x-2)/2)-16*sqrt(4*x-xˆ2)-(x-2)*4/2*sqrt(4*x-xˆ2)+
Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America
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