anonymous
  • anonymous
help me to solve this question... Find the total area between the curve y=1-x^2, and the x-axis over the interval (0,2)...
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
you have to integrate the given curve's equation in the interval (0,2) \[\int\limits_{0}^{2}1-x^2 = (2-0) + (-8/3 + 0) = 2 - 8/3 = -2/3\] Since are cannot be negative, area = 2/3 sq.units
anonymous
  • anonymous
sorry I'm little confused while typing equations on OpenStudy..so I've been a little late in answering
anonymous
  • anonymous
oo its ok..the working just like that AbhimanyuPudi ?

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anonymous
  • anonymous
may be u have to put another step in between..showing the integration.. \[\int\limits_{0}^{2}1-x^2 = x(from 0 \to 2) - x^3/3 (from 0 \to 2)\]
anonymous
  • anonymous
the negative sign in the answer indicates that the area is formed below the x-axis
RadEn
  • RadEn
for this case, first u have to figure out of the function y=1-x^2 |dw:1355817094537:dw| so, the total area = A1 + A2
shubhamsrg
  • shubhamsrg
i dont think you'll have to consider case of negative area here separately , so integrating directly from 0 to 2 should be correct..i may be wrong though..
shubhamsrg
  • shubhamsrg
forexample, integral(cosx) from x=0 to pi = 0 ..-ve and +ve areas cancel..
RadEn
  • RadEn
the result will be different if u use integration (0,2) with i said above :)
shubhamsrg
  • shubhamsrg
i know, i am saying if we integrate directly from 0 to 2, we will get correct ans.
RadEn
  • RadEn
no, @shubhamsrg for A1 = [x-1/3*x^3] [0,1] = 2/3 for A2 = [1/3*x^3-1] [1,2] = 4/3 so, total = 2/3 + 4/3 = 6/3 = 2
shubhamsrg
  • shubhamsrg
why will you treat negative area separately ? area can be -ve during integration!
RadEn
  • RadEn
because the rule, if u want calculate area in under x-axist, u have to give -ve in front integral (because the integration will be -ve also), so we get positive area
anonymous
  • anonymous
ok2 which one i should follow?
RadEn
  • RadEn
btw, for A1 i take int (f(x)) dx [0,1] and A2 i take int(-f(x)) dx [1,2]
shubhamsrg
  • shubhamsrg
so if ask you integral(cos x) from 0 to pi? ans according to you should be 2 right ?
anonymous
  • anonymous
I absolutely agree with @RadEn as we have to check the position of the area :)
anonymous
  • anonymous
Yes, A = 2 unit square!
RadEn
  • RadEn
but Abhimanyu's job not 2, but 2/3 :)
shubhamsrg
  • shubhamsrg
i just wanted to confirm : http://www.wolframalpha.com/input/?i=integral+%28cosx%29+from+0+to+pi
anonymous
  • anonymous
@sha0403 I leave the computing part for you, questions?
shubhamsrg
  • shubhamsrg
yes i have a question// why is wolfram giving value of integral =0 ? -ve is also real no.,, -ve area we do study, -ve indicates direction..please someone clarify..
RadEn
  • RadEn
@shubhamsrg , is it possible the area be 0 :)
shubhamsrg
  • shubhamsrg
http://www.wolframalpha.com/input/?i=integral+%28cosx%29+from+x%3D+pi%2F2+to+3pi%2F2
shubhamsrg
  • shubhamsrg
and also, it'll be 0 when you add together the +ve and -ve areas!
RadEn
  • RadEn
if just processing integration, yeah that's right but this case to find the area, so impossible be 0 or negative
shubhamsrg
  • shubhamsrg
i see what you mean,,hmm.. now i am also thinking if we go by my methodology , to find area of a circle, suppose x^2 + y^2 =1 , area turns out to be 0 i see..hmm you were right,,we got the take the absolute values..my apologies..
anonymous
  • anonymous
@shubhamsrg I'm not a fan of worf, honestly it's just a simple calculation!
shubhamsrg
  • shubhamsrg
i have maybe understood the concept sir,,sorry for the confusion..
anonymous
  • anonymous
ok thanks a lot for you guys for help me... =)
RadEn
  • RadEn
very welcome ... ::)

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