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Problem 42 Easy Difficulty

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{1}^4 [3^2 - (3 - \sqrt{x})^2] dx $

Name: each integral represents the volume of a solid describe the solid pi displaystyle int_14 32 3 sqrtx2
Uploaded: 2019-12-14
Duration: 28 s
Channel: Numerade
Description: Each integral represents the volume of a solid. Describe the solid. $ \pi \displaystyle \int_{1}^4 [3^2 - (3 - \sqrt{x})^2] dx $

Answer

The solid is obtained by rotating the region bounded by $y=3-\sqrt{x}$ and
$y=3$ in the interval $[1,4]$ about $x$ -axis

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Video Transcript

We know that when we're looking integration with respect to X, we know rotation is about the X axis, not the y axis. Therefore, we know we have an outer and inner radius out of radius is three and a radius is three mine escort of acts. Therefore, we know we obtained this by rotating the region around. Why is three months skirt of X and why is three in the interval 14 about the X axis?

Amrita B.

Topics

Applications of Integration

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Problem

A CAT scan produces equally spaced cross-sectiona…

Problem 42 Easy Difficulty

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{1}^4 [3^2 - (3 - \sqrt{x})^2] dx $

Answer

The solid is obtained by rotating the region bounded by $y=3-\sqrt{x}$ and
$y=3$ in the interval $[1,4]$ about $x$ -axis

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Caleb E.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 6

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Caleb E.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

A CAT scan produces equally spaced cross-sectiona…

Problem 42 Easy Difficulty

Each integral represents the volume of a solid. Describe the solid. $ \pi \displaystyle \int_{1}^4 [3^2 - (3 - \sqrt{x})^2] dx $

Answer

The solid is obtained by rotating the region bounded by $y=3-\sqrt{x}$ and$y=3$ in the interval $[1,4]$ about $x$ -axis

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Caleb E.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 6

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Caleb E.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{1}^4 [3^2 - (3 - \sqrt{x})^2] dx $

The solid is obtained by rotating the region bounded by $y=3-\sqrt{x}$ and
$y=3$ in the interval $[1,4]$ about $x$ -axis