Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
$ x = -3y^2 + 12y - 9 $ , $ x = 0 $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Amrita Bhasin
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
04:32
Wen Zheng
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 3
Volumes by Cylindrical Shells
University of Michigan - Ann Arbor
University of Nottingham
Idaho State University
Boston College
Lectures
05:10
Use the method of cylindri…
10:50
01:13
00:02
01:19
00:03
03:16
for this question, It may be helpful to draw a diagram. We can see our heightened our with and we can see are shaded region like this on We can see that the radius is gonna be why and the height is gonna be negative. Three y scored post 12 Why minus nine formula for volume Just to refresh your memory to pi times the intro from our bounds. In this case, it's 123 times radius times height. Now plug it Radius is why height is negative. Three y squared plus 12. Why minus nine And then we know this is gonna be multiplied by D. Why this gives us to pile on the outside Thames, the integral from 1 to 3. What's simple, finest negative Three. Why cubed plus 12 y squared minus nine. Why do you why, Okay, now that we integrate, we know we integrate by using the power rule, which means we increase the expert by ones and this gets increase it before divide by the new exponents. We do that for each of the three terms in this context, keeping in mind that our constant constituents down the outside now it's important that we plug in. We know we have two bounds to plug in. It's always top bound, minus the bottom bound when we are doing into role. So if this is the top bound, we are subtracting the bottom bounce again. It's the same constant on the outside that stays the same for both of them, and then we're playing in the two values. This is equivalent to 16 pie, which is R V.
View More Answers From This Book
Find Another Textbook
01:03
Karen bakes cookies. She has observed that the number of cookies that turn o…
00:41
a climber starts decending from 533 feet above sea level and keeps going unt…
00:18
Lydia made $56,750 last year. She paid $1200 in student loan interest and ma…
01:46
Cary is 9 years older than Dan. In 7 years, the sum of their ages will equal…
00:46
What is the most direct use of a compass in geometric constructions?A) t…
01:08
3 times the measure of an angle is 14 less than the measure of its complemen…
A company manufactures replacement parts for construction cranes. The fixed …
00:59
The temperature of a freezer started at 18ºC. After cooling for a few hours,…
00:52
What is the axis of symmetry of h(x) = –2x2 + 12x – 3?
01:15
Instructions:Type the correct answer in the box. Use numerals instead of wor…