MATH 221 Harvard University Mathematics Integral Questions Hello,I have attached all the questions that I need help with. please let me know if you have an

MATH 221 Harvard University Mathematics Integral Questions Hello,I have attached all the questions that I need help with. please let me know if you have any questions. M221_Sum Homework Assignment 10 (15.3,15.5,15.6) – Math 221, section 25, Summer 2 2020 | WebAssign
1.
[–/1 Points]
DETAILS
SCALCET8 15.3.007.
MY NOTES
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ASK YOUR TEACHER
PRACTICE ANOTHER
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the given integral by changing to polar coordinates.
2x2y dA, where D is the top half of the disk with center the origin and radius 4.
D
2.
[–/1 Points]
DETAILS
SCALCET8 15.3.008.
MY NOTES
Evaluate the given integral by changing to polar coordinates.
(2x − y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 16 and the lines x = 0 and y = x
R
3.
[–/1 Points]
DETAILS
SCALCET8 15.3.009.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the given integral by changing to polar coordinates.
R
sin(x2 + y2) dA, where R is the region in the first quadrant between the circles with center the origin and radii 2 and 4
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M221_Sum Homework Assignment 10 (15.3,15.5,15.6) – Math 221, section 25, Summer 2 2020 | WebAssign
4.
[–/1 Points]
DETAILS
SCALCET8 15.3.014.
MY NOTES
7/20/20, 4:47 PM
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the given integral by changing to polar coordinates.
D
5.
2
2
2
2
x dA, where D is the region in the first quadrant that lies between the circles x + y = 4 and x + y = 2x
[–/1 Points]
DETAILS
SCALCET8 15.5.003.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Find the area of the surface.
The part of the plane 3x + 13y + z = 39 that lies in the first octant
6.
[–/1 Points]
DETAILS
SCALCET8 15.5.007.
Find the area of the surface.
The part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and x2 + y2 = 25.
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M221_Sum Homework Assignment 10 (15.3,15.5,15.6) – Math 221, section 25, Summer 2 2020 | WebAssign
7.
[–/1 Points]
DETAILS
SCALCET8 15.6.501.XP.
7/20/20, 4:47 PM
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the iterated integral.
1
0
8.
2x
x
y
15xyz dz dy dx
0
[–/1 Points]
DETAILS
SCALCET8 15.6.502.XP.MI.
Evaluate the iterated integral.
π/2
0
9.
y
0
[–/1 Points]
x
0
8 cos (x + y + z) dz dx dy
DETAILS
SCALCET8 15.6.009.
Evaluate the triple integral.
y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}
E
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M221_Sum Homework Assignment 10 (15.3,15.5,15.6) – Math 221, section 25, Summer 2 2020 | WebAssign
10.
[–/1 Points]
DETAILS
SCALCET8 15.6.013.
MY NOTES
7/20/20, 4:47 PM
ASK YOUR TEACHER
PRACTICE ANOTHER
Evaluate the triple integral.
5xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y =
E
11.
[–/1 Points]
DETAILS
SCALCET8 15.6.504.XP.
MY NOTES
ASK YOUR TEACHER
x , y = 0, and x = 1
PRACTICE ANOTHER
Evaluate the triple integral.
E
12.
2xy dV, where E is bounded by the parabolic cylinders y = x2 and x = y2 and the planes z = 0 and z = 5x + y
[–/11 Points]
DETAILS
SCALCET8 15.6.017.MI.SA.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
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
Evaluate the triple integral.
E
x dV, where E is bounded by the paraboloid x = 8y2 + 8z2 and the plane x = 8.
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M221_Sum Homework Assignment 10 (15.3,15.5,15.6) – Math 221, section 25, Summer 2 2020 | WebAssign
13.
[–/1 Points]
DETAILS
SCALCET8 15.6.019.
MY NOTES
7/20/20, 4:47 PM
ASK YOUR TEACHER
PRACTICE ANOTHER
Use a triple integral to find the volume of the given solid.
The tetrahedron enclosed by the coordinate planes and the plane 11x + y + z = 5
14.
[1/1 Points]
MY NOTES
DETAILS
PREVIOUS ANSWERS
ASK YOUR TEACHER
SCALCET8 15.6.027.
PRACTICE ANOTHER
Sketch the solid whose volume is given by the iterated integral.
1
0
1− x
0
3 − 3z
0
dy dz dx
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M221_Sum Homework Assignment 10 (15.3,15.5,15.6) – Math 221, section 25, Summer 2 2020 | WebAssign
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