Q 45 The iterated integrals use spher... [FREE SOLUTION]

Chapter 13: Q 45 (page 1067)

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

Short Answer

Expert verified

The region represents inside the upward 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 ${鈭�}_{0}^{\frac{蟺}{4}} {鈭�}_{0}^{2 蟺} {鈭�}_{0}^{3 s e c 胃} f (蚁, 胃, 蠒) 蚁^{2} \sin 蠒 d 蚁 d 胃 d 蠒$

Step 2:Simplification

Given

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

According to order of integration

$蚁 = 0 t o 蚁 = 3 s e c 胃$

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

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

This represents equation of right circular cone

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

Also $蠒$ varies from $蠒 = 0 t o 蠒 = \frac{蟺}{4}$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Step 1:Given information

Step 2:Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

91影视

The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.鈭�0蟺4鈭�02蟺鈭�03sec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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

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