Please explain step by step in detail 2. Refer to the figure and find the volume obtained by rotating the given region about thespecified line.R2 about BCа.yAВ(1, 1)R3 about OCC(0, 1)R2b.y = %R3A(1, 0)

a) Given that, the radius r=1-x4 and the region is lies between a=0 and b=1. Obtain the area of the…

Answered: 2. Refer to the figure and find the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please explain step by step in detail

2. Refer to the figure and find the volume obtained by rotating the given region about the
specified line.
R2 about BC
а.
yA
В(1, 1)
R3 about OC
C(0, 1)
R2
b.
y = %
R3
A(1, 0)

Expert Solution

Step 1

Given that, the radius $r = 1 - \sqrt[4]{x}$ and the region is lies between a=0 and b=1.

Obtain the area of the region $R_{2}$ .

$\begin{array}{rcl} A (x) & = & π {(1 - \sqrt[4]{x})}^{2} \\ = & π (1 + \sqrt{x} + 2 \sqrt[4]{x}) \\ = & π (1 + {(x)}^{\frac{1}{2}} + 2 {(x)}^{\frac{1}{4}}) \end{array}$

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