Question
Asked Dec 7, 2019
10 views
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y = 4x² and 2x+y = 6 about the X-axis.
Volume =
help_outline

Image Transcriptionclose

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y = 4x² and 2x+y = 6 about the X-axis. Volume =

fullscreen
check_circle

Expert Answer

Step 1

Find the volume rotating the region curve and line about x-axis.

If the rotation is about x-axis, then the cylinder is horizontal.

help_outline

Image Transcriptionclose

Volume of integral is, V = [ 2a yg(y)\dy Where, y=radius x=g(y)is the height dy = thickness

fullscreen
Step 2

Substitute in terms of x, in curve and the line.

help_outline

Image Transcriptionclose

Given: y=4x2 ;2x+y=6 =x=±, 4 ;2x =6-y 6-y ;x= →x=±Vy 2 2 Equating the two equations we get y values +V _ 6-y 2 2.

fullscreen
Step 3

Take positive value an...

help_outline

Image Transcriptionclose

y 6-y 2 Jy =6-y Squaring on both sides, y=36–12y+y² y2 -13y+36=0 y=4and y=9(doen't statis fy). So, y=4. Similarly solve. Jy _6-y - we get y=9. It is rotating about x-axis, so, y=0.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Other

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add