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

(a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.(b) Use your calculator to evaluate the integral correct to five decimal places.

$ y = x $ , $ y = \frac{2x}{(1 + x^3)} $ ; about $ x = -1 $

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

02:33

Wen Zheng

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 3

Volumes by Cylindrical Shells

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

Boston College

Lectures

02:30

(a) Set up an integral for…

01:36

00:54

02:57

0:00

Set up an integral for the…

02:34

03:32

01:20

00:55

we know that we need to first find the intersection points, which means that if acts is two acts over one plus x cubed again, we're setting. If wise acts and wise to x over one plus x cube, we're setting the why equal to the y in terms of X. So for X, we end up with acts. Times X cubed minus one is zero and factored form, which gives us two values for ax zero and one. That's good. The's There are two bounds. Now we know the radius of each cylinder is X minus negative one, which is the same thing as X plus one. We know the height is gonna be two acts over one plus X cubed minus acts. Which means now we know we can write the integral as two pi times integral from 01 of X plus one against our times H So we're literally just putting it. This is R H is two acts over one plus X cubed minus axe. So just our terms. It's just these two values plugged in times. Divac's okay, this was part A was right. The interval part B is putting into your calculator. We're gonna put it into a graphing calculator. On we get 2.36164 and you can plug in exactly what we just wrote. If you have a graphing calculator is the same thing as two pi times two pi over three spurt of three minus five Sex But you can literally just plug in this whole integral into your calculator.

View More Answers From This Book

Find Another Textbook

03:31

jasmine used 3/4 kg of the eggplant for inihaw, 1/2 kg for pinakbet and 1/8 …

03:09

Rohan travelled 2/5 of his journey by train, 1/3 by a taxi, 1/6…

01:02

if 0.32 part of a bottle holds 125 ml the full capacity of the bottle is

if alpha and beta are the roots of the equation x3 - px2 + qx -r = 0. if alp…

02:38

An examination paper with 10 questions consists of 6 questions in Agebra and…

01:05

. Find the effective rate of interest if the nominal rate of interest is 8.4…

02:56

Who is responsible for metrics data preparation ?(a) Service Delivery Manage…

01:06

HCF and LCM of two numbers are 48 and 384 respectively. IF one of the number…

01:24

Sum of two numbers is 105. If one exceeds the other by 25. Find the number

02:58

Choose a real number uniformly at random in the interval [2,6] and call it X…