Hello...

Could you please help me out with this integral calculus... there is a though in this question...

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- May 31st 2007, 02:44 AMWhite DevilPlease I need help with this integral calculus...
- May 31st 2007, 02:51 AMearboth
- May 31st 2007, 03:02 AMWhite Devil
Sorry, I forgot to say the answer is not 0 nor 4....:confused:

- May 31st 2007, 03:06 AMCaptainBlack
Your question is, evaluate:

$\displaystyle

\int_{-2}^2 x\ dx= \left. \frac{x^2}{2}\right|_{-2}^2 = 2-2 = 0

$

Now why are you having problems with this? This question is about as

simple a definite integral as you are going to see and if you are having

problems with it you need more help than just being shown the solution.

RonL - May 31st 2007, 03:10 AMWhite Devil
The answer is not 0... the teacher said there is a though in it...

- May 31st 2007, 03:22 AMchogo
hey white devil the answer is definitely zero and not anything else

- May 31st 2007, 03:29 AMWhite Devil
Well the thing is our teacher said he will give 5 marks to who will answer it... and some students did it...

- May 31st 2007, 04:30 AMRich B.
Hi:

I am a teacher and such status does not protect me from being wrong. Nor does it do so for your teacher (else, he/she has one terrific contract!).

Now, picture the graph of y=x on the interval [-4, 4]. As the function is symmetric about the origin, the integral from -4 to 0 is necessarily opposite that from 0 to 4. The sum of two opposites is, of course, zero.

Regards,

Rich B. - May 31st 2007, 04:34 AMCaptainBlack
- May 31st 2007, 05:00 AMThePerfectHacker
- May 31st 2007, 05:06 AMearboth
Hello,

it's me again. If the answer isn't zero the only possibility I can think of is that you should calculate the area which is enclosed by y = x and x = -2 and x = 2.

The straight line with the equation y = x has a zero at x = 0. Thus you have to split the integral into 2 parts:

$\displaystyle \left| \int_{-2}^0 x dx \right| +\left| \int_{0}^2 x dx \right| =\left| \left. \frac{1}{2}x^2 \right|_{-2}^0 \right| +\left| \left. \frac{1}{2}x^2 \right|_{0}^2 \right| = 2 + 2 = 4$ - May 31st 2007, 05:46 AMWhite Devil
earboth you're right :) I have asked in other forum (Arabic one) and they told me the answer and it's exactly as you did...

But could you please make it graphical? - May 31st 2007, 06:21 AMCaptainBlack
- May 31st 2007, 11:36 AMearboth
- May 31st 2007, 12:09 PMWhite Devil
Thank you earboth that's what I asked for... Thanks all...