anonymous
  • anonymous
use integration to calculate the area bounded in the first region xy between these lines and curves x=2-y^2 x=1 x=0
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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reemii
  • reemii
|dw:1370098127422:dw| changing the roles of x and y, it's just a simple integral.
reemii
  • reemii
|dw:1370098257890:dw|
reemii
  • reemii
see you later @amrmagdy

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Luigi0210
  • Luigi0210
couldn't we use dy?
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reemii
  • reemii
you can use 'dy', I'm just more used to go back to the notation "dx".
reemii
  • reemii
sure. |dw:1370098540447:dw| just find a et b, and you can start integrating.
reemii
  • reemii
you have to find a and b. (a is the '>0' number such that x(a) = 1.) (b is the '>0' number such that x(b) = 0.) (just solve)
reemii
  • reemii
look at the picture+equation "x(a)=1." You must understand that one your own.
reemii
  • reemii
|dw:1370098834335:dw|
reemii
  • reemii
on*
Luigi0210
  • Luigi0210
|dw:1370098847713:dw| I would say find the are inside, then subtract it from the other area \[\int\limits_{0}^{2}2-y^2dy-\int\limits_{1}^{2}(2-y^2)-1dy\]
reemii
  • reemii
|dw:1370099063315:dw| that's the area to compute. you can see it as luigi says: big area - small area |dw:1370099097697:dw| or two little pieces of same size|dw:1370099132594:dw| + a rectangle choose what you prefer. (x(a)=1 <-> 2-a^2 = 1 <-> a^2 = 1 <-> a=±1). same thing for b
Luigi0210
  • Luigi0210
I am the worst in calculus :l
Luigi0210
  • Luigi0210
@amrmagdy where did you go? D:
reemii
  • reemii
@Luigi0210 i tihnk the integral you typed above is not the area.
Luigi0210
  • Luigi0210
Like I said, the worst in calculus.. .-.
reemii
  • reemii
you probably meant \[ \text{Area} = \int_{-\sqrt2}^{\sqrt2} (2-y^2) \,dy - \int_{-1}^1 (2-y^2-1) \,dy \] the \(y\) ranges from -sqrt2 to sqrt2.
reemii
  • reemii
@loser66
Luigi0210
  • Luigi0210
darn it -_-
reemii
  • reemii
|dw:1370100344436:dw| if they gave \(y\) in terms of x it would be a bit simpler
reemii
  • reemii
a bit more "pro" @Loser66
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reemii
  • reemii
i know, you're right, the drawings here look so c--ppy. ;p
reemii
  • reemii
it's useful for the ones who will read it, they'll understand better what happens. you can leave them.
Luigi0210
  • Luigi0210
This is why I use my color graph 66.. they'd rather see a real graph instead of my crappy hand drawn ones

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