Need help to solve another trig problem to find area on a graph. 6.1.29Find the volume of the solid generated by revolving the region enclosed by x=V35 y, x = 0, y = - 4, and y = 4 about the y-axis.The volume is cubic unit(s).(Type an exact answer, using radicals and t as needed.)

step:-1 Disk Method:- Volume of the solid revolving about y-axis is V=π∫abx2dy Now, given that…

Answered: Find the volume of the solid generated…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

100%

Need help to solve another trig problem to find area on a graph.

6.1.29
Find the volume of the solid generated by revolving the region enclosed by x=
V35 y, x = 0, y = - 4, and y = 4 about the y-axis.
The volume is cubic unit(s).
(Type an exact answer, using radicals and t as needed.)

Expert Solution

Step 1

step:-1

Disk Method:- Volume of the solid revolving about y-axis is

$V = π \int_{a}^{b} x^{2} dy$

Now, given that $x = \sqrt{35} y^{2}, x = 0, y = - 4, y = 4$

The region rotated about y-axis is ABOC as it is the region lie between x= 0 and y=-4, y=4.

Step:-2

Here, y lies between -4 to 4 that is, $- 4 \leq y \leq 4$ , So,

$V = \int_{- 4}^{4} {πx}^{2} dy = \int_{- 4}^{4} π {(\sqrt{35} y^{2})}^{2} dy = \int_{- 4}^{4} π (35 y^{4}) dy V = 35 π \int_{- 4}^{4} y^{4} dy = 35 π {[\frac{y^{5}}{5}]}_{- 4}^{4} = \frac{35 π}{5} (4^{5} - {(- 4)}^{5}) = \frac{35 π}{5} (1024 + 1024) = 14, 336 π V = 14, 336 π$

Step by step

Solved in 2 steps with 1 images

Knowledge Booster

$Paths and Circuits$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions