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Math Help - Calculate area of x-y

  1. #1
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    Calculate area of x-y

    Could someone please check my work?

    \int \int_D (x-y) dA

    where D is bounded by y=\sqrt{x} and y=x^2


    I evaluated the double integral as
    \int_0^1 \int_{x^2}^{\sqrt{x}} (x-y) dy dx

    Solving the definite integral, the answer got was \frac{1}{15}.

    Is this correct?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Calculate area of x-y

    Quote Originally Posted by tammyl View Post
    Could someone please check my work?

    \int \int_D (x-y) dA

    where D is bounded by y=\sqrt{x} and y=x^2


    I evaluated the double integral as
    \int_0^1 \int_{x^2}^{\sqrt{x}} (x-y) dy dx

    Solving the definite integral, the answer got was \frac{1}{15}.

    Is this correct?
    Check your math. The answer is 0.

    -Dan
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  3. #3
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    Re: Calculate area of x-y

    Scary that I manage the calculus and mess up the adding of fractions.

    Thank you greatly for your help!!!
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Calculate area of x-y

    Quote Originally Posted by tammyl View Post
    Scary that I manage the calculus and mess up the adding of fractions.

    Thank you greatly for your help!!!
    It's a more common problem than you might think.

    -Dan
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  5. #5
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    Re: Calculate area of x-y

    Quote Originally Posted by tammyl View Post
    Scary that I manage the calculus and mess up the adding of fractions.
    Yes, it means you are destined to be a mathematician!

    Be afraid. Be very afraid!

    Thank you greatly for your help!!!
    Thanks from topsquark
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