Answered: 4. Set-up and evaluate the definite…

4. Set-up and evaluate the definite integral that represents the area of the surface generated by revolving y _'n(y) lsys2 about the x-axis.

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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Question

100%

Is it possible to do #4? The GSA said it’s not but I just want to make sure.

1. Find the area bounded by the curves x= y´ and X = 3y-2. J
てメ)a4
2. Use the Disk/Washer Method to find the volume of the solid that results when the region bounded by y =
y = 3x is rotated about the x-axis.
Sx(42-4) dx
3. Use the Shell Method to find the volume of the solid that results when the region bounded by y= x and
y = 3x is rotated about the x-axis.
S2ex (42-ui)dx
4. Set-up and evaluate the definite integral that represents the area of the surface generated by revolving
y? !n(y)
X =
1sys2 about the x-axis.
4
5. Use integration by parts to evaluate the integrals. Sudu=uv-Judu
(a) fe* cos(2x)dx
nfe (c) f sec' (x)dx
(b) Ssin¯'(x)dx
6. Evaluate the integrals.by finding u, du and make a u-substitution in terms of u, then find the final answ
a) s
4+e2 dr
et
u=
du=
b) S
-dt
du=
u=
7. Evaluate the definite integrals by finding u and du, then make a u-substitution in terms of u that incluc
u-limits of integration.

Expert Solution

Step 1: Formula used and given.

Formula: The area of surface generated by revolving $x = f (y), a \leq y \leq b$ about $x -$ axis is given by,

$S = 2 π \int_{a}^{b} \sqrt{{(f' (y))}^{2} + 1} d y$ .

Given:

4. $f (y) = \frac{y^{2}}{4} - \frac{\ln (y)}{2}, 1 \leq y \leq 2$ and axis of rotation is $x -$ axis.

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