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sha0403
 2 years ago
help me to solve this question... Find the total area between the curve y=1x^2, and the xaxis over the interval (0,2)...
sha0403
 2 years ago
help me to solve this question... Find the total area between the curve y=1x^2, and the xaxis over the interval (0,2)...

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AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0you have to integrate the given curve's equation in the interval (0,2) \[\int\limits_{0}^{2}1x^2 = (20) + (8/3 + 0) = 2  8/3 = 2/3\] Since are cannot be negative, area = 2/3 sq.units

AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0sorry I'm little confused while typing equations on OpenStudy..so I've been a little late in answering

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0oo its ok..the working just like that AbhimanyuPudi ?

AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0may be u have to put another step in between..showing the integration.. \[\int\limits_{0}^{2}1x^2 = x(from 0 \to 2)  x^3/3 (from 0 \to 2)\]

AbhimanyuPudi
 2 years ago
Best ResponseYou've already chosen the best response.0the negative sign in the answer indicates that the area is formed below the xaxis

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4for this case, first u have to figure out of the function y=1x^2 dw:1355817094537:dw so, the total area = A1 + A2

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i 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
 2 years ago
Best ResponseYou've already chosen the best response.0forexample, integral(cosx) from x=0 to pi = 0 ..ve and +ve areas cancel..

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4the result will be different if u use integration (0,2) with i said above :)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i know, i am saying if we integrate directly from 0 to 2, we will get correct ans.

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4no, @shubhamsrg for A1 = [x1/3*x^3] [0,1] = 2/3 for A2 = [1/3*x^31] [1,2] = 4/3 so, total = 2/3 + 4/3 = 6/3 = 2

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0why will you treat negative area separately ? area can be ve during integration!

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4because the rule, if u want calculate area in under xaxist, u have to give ve in front integral (because the integration will be ve also), so we get positive area

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0ok2 which one i should follow?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4btw, for A1 i take int (f(x)) dx [0,1] and A2 i take int(f(x)) dx [1,2]

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0so if ask you integral(cos x) from 0 to pi? ans according to you should be 2 right ?

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0I absolutely agree with @RadEn as we have to check the position of the area :)

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, A = 2 unit square!

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4but Abhimanyu's job not 2, but 2/3 :)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i just wanted to confirm : http://www.wolframalpha.com/input/?i=integral+%28cosx%29+from+0+to+pi

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0@sha0403 I leave the computing part for you, questions?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0yes 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
 2 years ago
Best ResponseYou've already chosen the best response.4@shubhamsrg , is it possible the area be 0 :)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integral+%28cosx%29+from+x%3D+pi%2F2+to+3pi%2F2

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0and also, it'll be 0 when you add together the +ve and ve areas!

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.4if just processing integration, yeah that's right but this case to find the area, so impossible be 0 or negative

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i 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..

Chlorophyll
 2 years ago
Best ResponseYou've already chosen the best response.0@shubhamsrg I'm not a fan of worf, honestly it's just a simple calculation!

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0i have maybe understood the concept sir,,sorry for the confusion..

sha0403
 2 years ago
Best ResponseYou've already chosen the best response.0ok thanks a lot for you guys for help me... =)
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