Evaluate

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May 18th 2006, 12:09 AM
norivea

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Evaluate

I have attached an equation that requires an evaluation, I need help working this out, please!
May 18th 2006, 01:58 AM
CaptainBlack

Quote:

Originally Posted by norivea

I have attached an equation that requires an evaluation, I need help working this out, please!

$\int_0^{\pi} cos(x) dx$ .

Sketch this function over this range - you will see that it is anti-symmetric
about $\pi/2$ , so the integral is zero.

RonL
May 19th 2006, 01:42 PM
norivea

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Reply

So, is the answer:
May 19th 2006, 01:48 PM
TD!

No, you'd get:

$<br /> \int\limits_0^\pi {\cos xdx} = \left[ {\sin x} \right]_0^\pi = \sin \pi - \sin 0 = 0 - 0 = 0<br />$

You could have found this without integrating with CaptainBlack's argument, remember what an integral represents (signed area!).
May 19th 2006, 10:16 PM
norivea

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Reply

Ok thank you. I am just uncertain where I went wrong in my working. Could you look over my working to see where I went wrong? I have attached my original working.

Thanks again
May 19th 2006, 11:25 PM
CaptainBlack

Quote:

Originally Posted by norivea

Ok thank you. I am just uncertain where I went wrong in my working. Could you look over my working to see where I went wrong? I have attached my original working.

Thanks again

Why did you split the range of integration into $0-\pi/2$ , and
$\pi/2-\pi$ ?

The sign of $\cos$ is positive on the first of your sub-ranges and
negative on the second, so they cancel rather than add (since $\cos$
is anti-symmetric about $\pi/2$ ).

RonL
May 20th 2006, 06:07 PM
ThePerfectHacker

$\int^{\pi}_0 \cos x dx$
Thus,
$\left \sin x \right|^{\pi}_0$
Thus,
$\sin \pi -\sin 0=0-0=0$
May 20th 2006, 09:42 PM
earboth

Quote:

Originally Posted by norivea

Ok thank you. I am just uncertain where I went wrong in my working. Could you look over my working to see where I went wrong? I have attached my original working.
Thanks again

Hello,

according to your working you didn't evaluate the integral but you calculated the area which is enclosed by the x-axis, the graph of the cosine function and the lines x = 0 and x = pi. So you calculated:
$\int_{0}^{\pi}|{\cos(x)| dx$ which differs from your orginal integral.

Greetings

EB