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Math Help - Sketch the region and find the area

  1. #1
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    Sketch the region and find the area

    Sketch the region between -1 and 1 for 1/x^2 and find its area.

    So this is integral (-1 to 1) 1/x^2

    I can compute this and it comes to -2, but it is not integrable at x=0. So should I put for the area that is is infinite or what would the area be?
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    Sketch the region between -1 and 1 for 1/x^2 and find its area.

    So this is integral (-1 to 1) 1/x^2

    I can compute this and it comes to -2, but it is not integrable at x=0. So should I put for the area that is is infinite or what would the area be?
    you said it, it's not integrable there because it's not bounded on [-1,1].

    this splits as \int_{-1}^0\frac{dx}{x^2}+\int_0^1\frac{dx}{x^2}, then work this to see what leads to.
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  3. #3
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    But you also get when you do that, for example in the first integral

    -1/x and you can't plug 0 into there...so that brings me back to the question...is it just infinite area?
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  4. #4
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    Try splitting the integral into two and substituting the variable.

    So:
    \int_{-1}^0\frac{dx}{x^2}+\int_0^1\frac{dx}{x^2},<br />

    Substitute the lower limits of integration with variables, and take the limit as those variables approach zero from the left and right respectively.


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  5. #5
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    Still get division by 0
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  6. #6
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    Not if you take the limit as some variable approaches zero from the right or left. Then you will get infinity.
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