Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a. Write an integral that is the volume of the body with base the region of the $x, y-$ plane bounded by$$y_{1}=0.25 \sqrt{x} \sqrt[4]{2-x} \quad y_{2}=-0.25 \sqrt{x} \sqrt[4]{2-x} \quad 0 \leq x \leq 2$$and with each cross section perpendicular to the $x$ -axis at $x$ being a square with lower edge having endpoints $\left[x, y_{2}(x), 0\right]$ and $\left[x, y_{1}(x), 0\right]$ (see Exercise Figure 11.1.5A). (The value of the integral is $4 \sqrt{2} / 15$ ).b. Write an integral that is the volume of the body with base the region of the $\mathrm{x}, \mathrm{y}$ -plane bounded by$$y_{1}=0.25 \sqrt{x} \sqrt[4]{2-x} \quad y_{2}=-0.25 \sqrt{x} \sqrt[4]{2-x} \quad 0 \leq x \leq 2$$and with each cross section perpendicular to the $x$ -axis at $x$ being an equilateral triangle with lower edge having endpoints $\left[x, y_{2}(x), 0\right]$ and $\left[x, y_{1}(x), 0\right]$ (see Exercise Figure $11.1 .5 \mathrm{~B}$ ). (The value of the integral is $\sqrt{6} / 15$ ).

Calculus 2 / BC

Chapter 11

Applications of the Fundamental Theorem

Section 1

Volume

Applications of Integration

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

00:59

Consider a solid whose bas…

02:25

Use the general slicing me…

02:02

The region bounded between…

01:41

Find the volume of the sol…

00:34

For the following exercise…

00:44

01:31

02:40

04:02

01:33

Sketch the region bounded …

04:04

In Exercises 1 and $2,$ fi…

08:11

Evaluate the following int…

03:24

04:00

Find the area of the regio…

03:54

(a) Set up an integral for…

03:57

Use the region $R$ that is…

03:34

04:49

02:42

Write an iterated integral…

00:57

that's draw the region first. These curve is why equal to square roots off three minus sets and the wrath line is X equal to chew, since the shape off a cross section off the given solid is square with the inside while like these screen blinds in part a, the area a off X is Y squared, which is three minus x in part B. Here is the formula off volume according to general slicing method things that is protein between 0 to 2 and a affects is three minus X. So the volume is IT girl from 0 to 23 minus x the X uh

View More Answers From This Book

Find Another Textbook

Numerade Educator