Q 44 The iterated integrals use spher... [FREE SOLUTION]

Chapter 13: Q 44 (page 1067)

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.
${鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{1} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

Short Answer

Expert verified

The region represents sphere with second quadrant with the hemisphere below the $x y -$ plane of the sphere with radius 1 centered at origin

Step by step solution

Step 1:Given information

The given expression is ${鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{1} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

Step 2:Simplification

${鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{1} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

According to the order of integration

$鈬� 蚁 = 0 t o 蚁 = 1$

$鈬� \sqrt{x^{2} + y^{2} + z^{2}} = 1$

$鈬� x^{2} + y^{2} + z^{2} = 1^{2}$

This is a sphere equation with radius 1 centered at origin

Now,

$鈬� 胃$ varies from $0 t o \frac{蟺}{2}$

It means it is in second quadrant

Now,

$鈬� 蠎$ varies from $0 t o \frac{蟺}{2}$

these the region represents the hemisphere below the xy -plane of the sphere with radius 1 centered at origin

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91影视

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.
${鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{1} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

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91影视

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.鈭�0蟺2鈭�0蟺2鈭�01f蚁,胃,蠒蚁2sin蠒d蚁d胃d蠒

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Logic and Functions

Statistics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.
${鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{\frac{蟺}{2}} {鈭�}_{0}^{1} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$