The following for an integral ∫ 0 4 ( 16 − x 2 ) d x . a. What area does the integral represent?

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Answer 1

Question

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

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(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.

(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).

Answer 2

Question

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

Answer 6

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

Answer 7

Chapter 14.5, Problem 26AYU

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

Answer 8

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

Answer 9

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

Answer 10

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

Answer 11

To determine

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - Prob. 9AYU Ch. 14.1 - Prob. 10AYU

The following for an integral ∫ 0 4 ( 16 − x 2 ) d x . a. What area does the integral represent?

Solution Summary: The author explains how to find an integral by using a graphing utility to approximate its area.

Concept explainers

Videos

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.

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Chapter 14 Solutions

Additional Math Textbook Solutions

The following for an integral ∫ 0 4 ( 16 − x 2 ) d x . a. What area does the integral represent?

Solution Summary: The author explains how to find an integral by using a graphing utility to approximate its area.

Concept explainers

Videos

To find: The following for an integral ∫ 0 4 ( 16 − x 2 )dx . a. What area does the integral represent?

To find: The following for an integral ∫ 0 4 ( 16 − x 2 )dx . b. Provide a graph that illustrates this area.

To find: The following for an integral ∫ 0 4 ( 16 − x 2 )dx . c. Use a graphing utility to approximate this area.

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

a. What area does the integral represent?

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

b. Provide a graph that illustrates this area.

To find: The following for an integral $\int_{0}^{4} (16 - x^{2}) d x$ .

c. Use a graphing utility to approximate this area.