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

Find the volume of the solid bounded above by the surface $z=f(x, y)$ and below by the region $R$ in the $x$ -y plane. $f(x, y)=y, R: y=2 x, x=0,$ and $y=2$.

$$4 / 3$$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

Oregon State University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

01:51

Find the volume of the sol…

03:44

04:30

03:14

02:13

03:42

for this problem we are asked to find the volume of the solid bounded above by the surface, Z equals y and below by the region defined by Y equals two. X X equals zero and Y equals two in the xy plane. So plotting out our region are, we can see that this would be the projection into the xy plane. So we can set this up as the integral. From now. We have a few options but we can set this up as the integral from, let's say From 0 to 2 of the integral. From now integrating over X from zero up to now the line Y equals two. X would become the line X equals two or a by over two of why? Dx dy. So this will then become zero or the integral from 0 to 2 of Y X evaluated from zero to y over two. Do you know why? So this will then be integral from 0 to 2 of Y times Y over two. So why squared over two minus zero dy. Which will then give us why cubed over two times three. So y cubed over six, evaluated from 0 to 2, which gives us the final result then of 8/6. Which Can then be simplified down to 4/3

View More Answers From This Book

Find Another Textbook

01:17

A function is said to be homogeneous of degree $n$ if $f(\gamma x, \gamma y)…

03:45

Determine the area of the indicated region.Region bounded between $f(x)=…

02:29

Determine the area of the indicated region.Region bounded by $f(x)=2 / x…

03:22

The partial differential equation $c^{2} u_{x x}-u_{t t}=0$ where $c$ is a c…

02:59

Consider the parabola $f(x)=a x^{2},$ with $a>0 .$ When $x=b,$ call the $…

04:06

Consider the graph defined by $f(x)=a x^{n},$ with $a>0$ and $n \neq-1 .$…

01:39

08:40

Show that $u(x, t)=f(x-c t)+g(x+c t)$ is a solution to the wave equa$\operat…

02:01

01:41

Determine the region $R$ determined by the given double integral.$$\int_…