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Math Help - another area under curves

  1. #1
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    another area under curves

    y=x^2<br />
y=\frac{2}{x^2+1}<br />
    intersects at + or - 1
    so integral would be <br />
2\int_{-1}^1 \frac{2}{x^2+1}-x^2dx
    after reducing, I got 2\int_{-1}^1 \frac{1-x^2}{x^2+1}dx
    Don't know how to find anti derivative from here...

    I just looked in the back for the answer and it is pi-2/3
    is there some sort of trig identity going on....
    Last edited by dorkymichelle; December 12th 2010 at 01:17 AM.
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  2. #2
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    Quote Originally Posted by dorkymichelle View Post
    y=x^2<br />
y=\frac{2}{x^2+1}<br />
    intersects at + or - 1
    so integral would be <br />
2\int_{-1}^1 \frac{2}{x^2+1}-x^2dx
    after reducing, I got 2\int_{-1}^1 \frac{1-x^2}{x^2+1}dx
    Don't know how to find anti derivative from here...
    Personally, I don't know why you have that final line. It's unnecessary and also wrong. Just use the second last line (after fixing an obvious error in it) ....
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