anonymous
  • anonymous
how do you find the area enclosed by a line, a parabola, and the x-axis?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
integrate :)
anonymous
  • anonymous
i know but integrate what
myininaya
  • myininaya
we need to know what parabola and what line

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anonymous
  • anonymous
if you have x^2 from 0 to 1 its int (0 to 1) of x^2 dx
anonymous
  • anonymous
as an example
anonymous
  • anonymous
Find the area enclosed by \[y=\sqrt{2x}, y=6-2x, and the xaxis\]
myininaya
  • myininaya
first find where they intersect
anonymous
  • anonymous
but they intersect at three different places
amistre64
  • amistre64
those equation only intersect in one place :)
anonymous
  • anonymous
rearrange for x in the equations, your parabola will then be the lower limit, the straight line will be the upper limit and your y limits will be from 0 to the y component of the intersection point, then it is a trivial double integral
myininaya
  • myininaya
i will scan and show you my drawing
myininaya
  • myininaya
1 Attachment
anonymous
  • anonymous
\[\int\limits_{0}^{y component of intersection}\int\limits_{(y^2)/2}^{1/2y+3}..and so on\]
myininaya
  • myininaya
i always have to draw picture first
anonymous
  • anonymous
me too by visual inspection you can simplify the problem a lot
myininaya
  • myininaya
dana, have you looked at the pic?
myininaya
  • myininaya
i also put what i integrated
myininaya
  • myininaya
oops that second integral should e from 2 to 3 i messed up my line a bit
anonymous
  • anonymous
\[\int\limits_{0}^{2}\int\limits_{.5y^2}^{-0.5y-3}dxdy\]
anonymous
  • anonymous
yeaa that makes sence now, thank you!
myininaya
  • myininaya
there was not suppose to be an e in that sentence lol
myininaya
  • myininaya
because the x intercept of that y=6-2x is 3 not 4
anonymous
  • anonymous
yea his way if fine too, the double integral is just another way you can check your answer
myininaya
  • myininaya
she*
myininaya
  • myininaya
her*
anonymous
  • anonymous
oh sorry
anonymous
  • anonymous
wasn't paying attention to the name there sorry
anonymous
  • anonymous
but on the other hand that double integral is pretty epic? can someone be my fan i think i deserve it for going all out on this question
myininaya
  • myininaya
i will be ur fan
anonymous
  • anonymous
thanks! i'm your fan too.
anonymous
  • anonymous
helped people a few times but it seems a lot of people just make an account to ask a question and then leave without saying thank you
myininaya
  • myininaya
your welcome dana lol
myininaya
  • myininaya
he didnt become our fan :(
myininaya
  • myininaya
dana, if you come back you could have done int(3-y/2-y^2/2,y=0..2) and got the same thing you could have look at the functions as if y-axis was x-axis
anonymous
  • anonymous
ohh thats true, to switch the problem around. and i did say thank you, for the record. you all were a lot of help! :)
myininaya
  • myininaya
lol im sorry i didn't notice im an idiot
anonymous
  • anonymous
are aunder a curve, use integration & subtract lower curve from upper

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