Register to reply 
Supposedly simple double integral 
Share this thread: 
#1
Nov307, 02:56 PM

P: 4

double integral of xy dA
in the triangular region of (0,0), (3,0), (0,1). my problem that I am having is finding the limits I am suposed to find dx or dy in. I figure I should use 0 to 3 for dx, but then i do dy from 0 to what? Help appreciated. 


#2
Nov307, 03:25 PM

Sci Advisor
P: 1,232

Try drawing a picture of the region. Then, for a given value of x, what values of y lie within the region? This gives you the limits of integration for y, given x. (Of course, you must then do the y integral before you do the x integral.)



#3
Nov307, 08:44 PM

P: 4

so then the parameters for y would be: 0 to x/3?



#4
Nov407, 06:33 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,682

Supposedly simple double integral
Yes, because the upper boundary is the line y= x/3.
It is a very good exercise to "swap" the limits of integration. Suppose you wanted to integrate with respect to x first and then y? Clearly to cover the entire triangle, you must take y going from 0 to 1. For each y, then, x must go from the left boundary, x= 0, to the "right" boundary which is still that line y= x/3. That is, x must go from x= 0 to x= what? Do the integral of xy both ways and see if you get the same thing. 


#5
Nov407, 04:22 PM

P: 4

I used the parameters dy= 0 to 1 and dx= 0 to 3y+3 and got 2.375.
the answer was wrong. I did it the other way with dy=0 to x/3+1 and dx= 0 to 3 and got another wrong answer. what am I doing wrong? 


Register to reply 
Related Discussions  
Double Integral Help  Calculus  1  
Double integral.  Calculus  2  
Simple (supposedly) circuit analysis involving a C.C.V.S.  2 I.V.S.  I.C.S  6 Res.  Engineering, Comp Sci, & Technology Homework  13  
Double integral  Calculus & Beyond Homework  6  
Simple (supposedly) pendulum with unknown length and kinetic energy...  Introductory Physics Homework  4 