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Math Help - evaluate the integral

  1. #1
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    evaluate the integral

    \int_{-5}^5 (8-|x|) dx
    the answer is 55 but I am hving throuble getting to the solution.
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  2. #2
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    Re: evaluate the integral

    Quote Originally Posted by delgeezee View Post
    \int_{-5}^5 (8-|x|) dx
    the answer is 55 but I am hving throuble getting to the solution.
    Since you have a even function:

    \int_{-5}^5 (8-|x|) dx=2\int_{0}^5 (8-|x|) dx=2\int_{0}^5 (8-x) dx

    CB
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  3. #3
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    Re: evaluate the integral

    Quote Originally Posted by delgeezee View Post
    \int_{-5}^5 (8-|x|) dx
    the answer is 55 but I am hving throuble getting to the solution.
    |x| =\begin{cases} -x, & \text{if }x \leq 0 \\x, & \text{if}x\geq 0\end{cases}

    I=\int\limits_{-5}^{0} (8+x)\, dx+ \int\limits_{0}^{5}(8-x)\, dx
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    Re: evaluate the integral

    Sorry! I can solve it using geometry, but I still need a little more help.


    The interval length I had before was 10/n, would it now change to 5/n ??



     \frac{5}{n} [\sum\limits_{k=1}^{n} (8+x) + \sum\limits_{k=1}^{n} (8-x) ]


    Using reimann's right sum (a+k* \Delta )

    does it matter which reimann sum I use?
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  5. #5
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    Re: evaluate the integral

    Why are you doing that? Are you required to reduce it to a Riemann's sum first? If so you should have told us that to start with.
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  6. #6
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    Re: evaluate the integral

    According to Captain Black's post, your area is 2\int_{0}^{5}(8-x)dx.

    Now, recall that \int_{a}^{b}f(x)dx=\lim_{n \to \infty}\sum_{i=1}^{n}f(x_i)\Delta x where \Delta x=\frac{b-a}{n} and x_i=a+i \Delta x.

    In this case

    a=0
    b=5
    \Delta x = \frac{5}{n}
    x_i=0+i\Delta x =\frac{5i}{n}
    f(x_i)=8-\frac{5i}{n}

    required area = 2 \times \lim_{n \to \infty}\sum_{i=1}^{n}( 8-\frac{5i}{n})\frac{5}{n}

    Evaluating this, you will get the value of the definite integral.
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  7. #7
    Grand Panjandrum
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    Re: evaluate the integral

    Quote Originally Posted by delgeezee View Post
    Sorry! I can solve it using geometry, but I still need a little more help.


    The interval length I had before was 10/n, would it now change to 5/n ??



     \frac{5}{n} [\sum\limits_{k=1}^{n} (8+x) + \sum\limits_{k=1}^{n} (8-x) ]


    Using reimann's right sum (a+k* \Delta )

    does it matter which reimann sum I use?
    Post the full question.

    CB
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  8. #8
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    Re: evaluate the integral

    Ti-89 says 55 you got the correct answer.
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  9. #9
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    Re: evaluate the integral

    Quote Originally Posted by CalBear12 View Post
    Ti-89 says 55 you got the correct answer.
    Yes, 55 is the correct answer, but the point is that delgeeze never got the answer.
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  10. #10
    Grand Panjandrum
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    Re: evaluate the integral

    Quote Originally Posted by sbhatnagar View Post
    Yes, 55 is the correct answer, but the point is that delgeeze never got the answer.
    I'm afraid most of CalBear12's posts partake of the nature of the one you are commenting upon. I'm hopping he will learn to read the original and the other posts in a thread more carefully before shooting-form-the-hip before he earns a weeks ban due to accumulated infractions.

    CB
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