My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 1st, 2017, 11:18 AM   #1
Newbie
 
Joined: Oct 2017
From: India

Posts: 1
Thanks: 0

Question on Multiple Integration

Hiiiee!!
I'mma. Jyoti,, from India. . .,,
Pursuing Btech I T. 1st year
Having some problems with my subjects,,,
I'll be glad if you help me out with this question. I'd attached the picture of the question as an attachment.
Attached Images
File Type: jpg IMG_20171001_234455.jpg (17.7 KB, 10 views)
Jyoti is offline  
 
October 1st, 2017, 02:38 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,397
Thanks: 546

Plot the limits of y on x-y graph. Look at what the limits would be if you did x first.
mathman is offline  
October 1st, 2017, 05:36 PM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,875
Thanks: 766

The integral as given takes x from 0 to 1 and, for each x, y from x to $\displaystyle \sqrt{2- x^2}$ (and it should be "dydx" not "dxdy"). In an xy-coordinate system, as mathman suggests, $x= 0$ and $x= 1$ are vertical lines, $y= x$ is a slant line, though (0, 0) and (1, 1), and $\displaystyle y= \sqrt{2- x^2}$, which is the same as $\displaystyle y^2= 2- x^2$ or $\displaystyle x^2+ y^2= 2$ is the circle with center at (0, 0) and radius $\displaystyle \sqrt{2}$. That circle intersects the line $y= x$ at (1, 1) and the line $x= 0$ at $\displaystyle (0, \sqrt{2})$. So $y$, overall, goes from 0 to $\displaystyle \sqrt{2}$ and, for each $y$, with $\displaystyle 0\le y\le 1$, $x$ goes from 0 to $y$, while with $\displaystyle 1\le y\le \sqrt{2}$, $x$ goes from 0 to $\displaystyle \sqrt{2- y^2}$.

The integral, with order of integration reversed, is $\displaystyle \int_0^1\int_0^{\sqrt{2- y^2}} \frac{x dxdy}{\sqrt{x^2+ y^2}}$.

Do you see why that is easier to integrate than the original form?

Last edited by skipjack; October 1st, 2017 at 07:20 PM.
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
integration, multiple, question



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Question about Multiple Integration VTech Real Analysis 1 December 6th, 2015 06:16 PM
Doubt with multiple integral and limits of integration szz Calculus 3 March 27th, 2015 01:29 PM
Multiple Choice Question lovetolearn Calculus 2 April 14th, 2012 02:33 PM
Multiple integration problem help!!!!! bballlj15 Calculus 1 April 30th, 2009 01:30 PM
calculus multiple question kingkos Algebra 4 December 31st, 1969 04:00 PM





Copyright © 2017 My Math Forum. All rights reserved.