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. 
October 1st, 2017, 02:38 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,397 Thanks: 546 
Plot the limits of y on xy graph. Look at what the limits would be if you did x first.

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 xycoordinate 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. 

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 