Q 46 The iterated integrals use spher... [FREE SOLUTION]

Chapter 13: Q 46 (page 1067)

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.
${鈭�}_{\frac{蟺}{4}}^{\frac{蟺}{2}} {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{3 c s c 胃} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

Short Answer

Expert verified

The region represents inside the downward opening right circular cone that has z-axis as its axis of symetry height 3 and radius 3

Step by step solution

Step 1:Given information

The given expression is ${鈭�}_{\frac{蟺}{4}}^{\frac{蟺}{2}} {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{3 c s c 胃} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

Step 2:Simplification

Given

${鈭�}_{\frac{蟺}{4}}^{\frac{蟺}{2}} {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{3 c s c 胃} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

According to order of integration

$蚁 = 0 t o 蚁 = 3 c s c 胃$

$鈬� \sqrt{x^{2} + y^{2} + z^{2}} = 3 c s c 胃$

$鈬� x^{2} + y^{2} + z^{2} = 3^{2} c s c^{2} 胃$

This represents equation of right circular cone

And $胃$ varies from $胃 = 0 t o 胃 = 2 蟺$

Also $蠒$ varies from $蠒 = \frac{蟺}{4} t o 蠒 = \frac{蟺}{2}$

From these the region represents inside the downward opening right circular cone that has z-axis as its axis of symetry height 3 and radius 3

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91影视

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.
${鈭�}_{\frac{蟺}{4}}^{\frac{蟺}{2}} {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{3 c s c 胃} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

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�蟺4蟺2鈭�02蟺鈭�03csc胃f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

Geometry

Probability and Statistics

Logic and Functions

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.
${鈭�}_{\frac{蟺}{4}}^{\frac{蟺}{2}} {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{3 c s c 胃} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$