Question about a double integral region

  • Thread starter Amaelle
  • Start date
  • #1
Amaelle
310
54
Homework Statement:
look at the image
Relevant Equations:
double integral
Greetings All!

I have a problem finding the correct solution at first glance

My error was to determine the region of integration , for doing so I had to the intersection between y= sqrt(x) and y=2-x

to do so
x=(2-x)^2
to find at the end that x=1 or x=5

while graphically we can see that the region start from x=0 they intersect in x=1 and never meet again!

could someone help me with my confusion ?

Thank you!
1644410525129.png

 

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Answers and Replies

  • #2
anuttarasammyak
Gold Member
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Drawing the region on xy plane would help you.
 
  • #3
Amaelle
310
54
Drawing the region on xy plane would help you.
yes this i what I done
I just want to know why my analitical results was wrong
 
  • #5
Delta2
Homework Helper
Insights Author
Gold Member
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The solutions are x=1 and x=4 but the x=4 solution is not accepted because we want 2-x to be greater than zero. Remember that the inequality is $$0\leq \sqrt x\leq y\leq 2-x$$
 
  • #6
Amaelle
310
54
The solutions are x=1 and x=4 but the x=4 solution is not accepted because we want 2-x to be greater than zero. Remember that the inequality is $$0\leq \sqrt x\leq y\leq 2-x$$
thanks a million! you nail it!
 

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