I want 3no ques answer. 3.) y = Vr, y = 3, x = 0 around the x axis.

Name: I want 3no ques answer. 3.) y = Vr, y = 3, x = 0 around the x axis.
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Description: I want 3no ques answer. 3.) y = Vr, y = 3, x = 0 around the x axis.

Answered: 3.) y = Vr, y = 3, x = 0 around the x…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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I want 3no ques answer.

3.) y = Vr, y = 3, x = 0 around the x axis.

Expert Solution

Step 1

To find: The volume of the solid that is generated by the revolving the given function $y = \sqrt{x}$ around the x axis.

Given information:

The curve of the function about the axis bounded by the $x = 0 and y = 3$ .

Concept Used:

The volume of the solid generated by the curve over the interval about the -axis is represented below:

$V = 2 π \int_{a}^{b} [f (y)] d y$ …… (1)

The power rule of integration $\int y^{n} d x = \frac{y^{n + 1}}{n + 1}$ is where x is the variable of the integration and n is the constant that is equal to -1 .

Step 2

First make the graph of the given function around the x-axis.

Step 3

Calculation:

The function in the terms of $f (y)$ as,

$\begin{matrix} y = \sqrt{x} \\ x = y^{2} \\ f (y) = y^{2} \end{matrix}$

The given values are $x = 0 and y = 3$ .

It is given the solid is generated in the first quadrant therefore, the limits for y in the first quadrant is from 0 to 3.

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