11/25/2019
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
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MATH 2163, section 61998, Fall 2019
INSTRUCTOR
Sec. 15.4: Integration in Other Coordinate Systems
(Calculus3Homework)
Ning Ju
Northern Oklahoma
College
Current Score
QUESTION
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17
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TOTAL SCORE
–/19
0.0%
Due Date
DECEMBER 14
11:48 PM CST
Assignment Submission & Scoring
Assignment Submission
For this assignment, you submit answers by question parts. The number of submissions remaining for each
question part only changes if you submit or change the answer.
Assignment Scoring
Your best submission for each question part is used for your score.
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11/25/2019
1.
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
–/1 points
RogaCalcET3 15.4.001.
My Notes
Sketch the indicated region D and integrate f(x, y) over D using polar coordinates.
f(x, y) =
2.
–/1 points
x2 + y2 ,
D: x2 + y2 ≤ 7
RogaCalcET3 15.4.003.
My Notes
Sketch the indicated region D and integrate f(x, y) over D using polar coordinates.
f(x, y) = 8xy,
3.
–/2 points
D: x ≥ 0, y ≥ 0, x2 + y2 ≤ 16
RogaCalcET3 15.4.005.
My Notes
Sketch the indicated region D and integrate f(x, y) over D using polar coordinates.
f(x, y) = y(x2 + y2)−1;
D: y ≥
7
, x2 + y2 ≤ 49
2
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11/25/2019
4.
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
–/1 points
RogaCalcET3 15.4.007.
My Notes
Find the volume of the wedge-shaped region on the figure below contained in the cylinder x2 + y2 = 81, and
bounded above by the plane z = x, and below by the xy-plane.
5.
–/1 points
RogaCalcET3 15.4.010.
My Notes
Integrate by changing to polar coordinates.
49 − x2
7
0
6.
tan−1
0
–/1 points
y
x
dy dx
RogaCalcET3 15.4.011.
My Notes
Integrate by changing to polar coordinates.
4
0
y
5x dx dy
0
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11/25/2019
7.
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
–/1 points
RogaCalcET3 15.4.017.Tutorial.
My Notes
Calculate the integral over the given region by changing to polar coordinates.
f(x, y) = |7xy|; x2 + y2 ≤ 1
Additional Materials
Tutorial
8.
–/1 points
RogaCalcET2 15.4.025.
My Notes
Let W be the region between the paraboloids z = x2 + y2 and z = 32 − x2 − y2. Compute the volume of W
using cylindrical coordinates.
9.
–/1 points
Evaluate
D
RogaCalcET3 15.4.027.
My Notes
2
2
x2 + y2 dA, where D is the domain in the figure below, if F: x + y = 16,
G:(x − 2)2 + y2 = 4, Rf = 4, and Rg = 2.
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11/25/2019
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
RogaCalcET3 15.4.029.
–/1 points
10.
Use cylindrical coordinates to calculate
My Notes
f(x, y, z) dV for the given function and region.
W
x2 + y2 ≤ 1,
f(x, y, z) = y;
y ≥ 0,
0≤z≤5
RogaCalcET3 15.4.033.
–/1 points
11.
x ≥ 0,
My Notes
Express the triple integral in cylindrical coordinates.
4 − x2
2
−2 −
4−
x2
9
f(x, y, z) dz dy dx
0
f(r cos(θ), r sin(θ), z)r dz dr
0
0
0
dθ
–/1 points
12.
RogaCalcET3 15.4.036.
My Notes
Express the triple integral in cylindrical coordinates.
9x − x2
9
0
0
x2 + y2
f(x, y, z) dz dy dx
0
f(r cos(θ), r sin(θ), z)r dz dr
0
dθ
0
0
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11/25/2019
13.
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
–/1 points
RogaCalcET3 15.4.051.
My Notes
Use spherical coordinates to calculate the triple integral of f(x, y, z) = z over the region
0 ≤ θ ≤ π,
6
14.
–/1 points
0 ≤ φ ≤ π,
2
3≤ρ≤4
RogaCalcET3 15.4.046.
My Notes
Use spherical coordinates to calculate the triple integral of f(x, y, z) over the given region.
f(x, y, z) = ρ−3;
15.
–/2 points
9 ≤ x2 + y2 + z2 ≤ 36
RogaCalcET3 15.4.045.
My Notes
Use spherical coordinates to calculate the triple integral of f(x, y, z) over the given region.
f(x, y, z) = y;
x2 + y2 + z2 ≤ 9,
x, y, z ≤ 0
Additional Materials
CalcClip
16.
–/1 points
RogaCalcET3 15.4.052.
My Notes
Find the volume of the region lying above the cone φ = π and below the sphere ρ = 2.
3
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11/25/2019
17.
Sec. 15.4: Integration in Other Coordinate Systems - MATH 2163, section 61998, Fall 2019 | WebAssign
–/1 points
RogaCalcET3 15.4.054.
My Notes
Calculate the volume of the cone in figure using spherical coordinates. Assume that R = 4, H = 5.
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