(a) To find: The area between the x -axis and the upper half of the ellipse for the given equation 4 x 2 + 9 y 2 = 36 by using the trapezoidal rule.

Question

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Answer 1

Question

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

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(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}. Calculate the integral f(x, y, z) dv. E

(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

Answer 2

Question

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Answer 6

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

Answer 7

Chapter 8.1, Problem 14E

To determine

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

Answer 8

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

Answer 9

To determine

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

Answer 10

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Answer 11

To determine

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

(a) To find: The area between the x -axis and the upper half of the ellipse for the given equation 4 x 2 + 9 y 2 = 36 by using the trapezoidal rule.

Solution Summary: The author explains how to find the area between the x -axis and the upper half of an ellipse by using the trapezoidal rule.

Concept explainers

Videos

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Want to see the full answer?

Chapter 8 Solutions

(a) To find: The area between the x -axis and the upper half of the ellipse for the given equation 4 x 2 + 9 y 2 = 36 by using the trapezoidal rule.

Solution Summary: The author explains how to find the area between the x -axis and the upper half of an ellipse by using the trapezoidal rule.

Concept explainers

Videos

(a) To find: The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

(b) To find: The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

(c) The techniques were more accurate after compare the result with area found by the formula for the area of the circle.

Want to see the full answer?

Chapter 8 Solutions

(a)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the trapezoidal rule.

(b)

To find:

The area between the x-axis and the upper half of the ellipse for the given equation 4x2+9y2=36 by using the Simpson’s Rule.

(c)

The techniques were more accurate after compare the result with area found by the formula for the area of the circle.