Math 2414 DHW 4
.pdf
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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
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