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Math Help - definite integral

  1. #1
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    definite integral

    find the value of
    a) A \approx \sum_{k = 1}^{n} f(x_{k}^*) \Delta x


    b)max
    \Delta{x_{k}}

    f(x)=x+1; a=0,b=4; n=3;
    Deltax_1=1,\ Deltax_2=1,\ Deltax_3=2\
    {x_{1}^*}=1/3,\ {x_{2}^*}=3/2,\ {x_{3}^*}=3

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by vinson24 View Post
    find the value of
    a) A \approx \sum_{k = 1}^{n} f(x_{k}^*) \Delta x


    b)max
    \Delta{x_{k}}

    f(x)=x+1; a=0,b=4; n=3;
    Deltax_1=1,\ Deltax_2=1,\ Deltax_3=2\
    {x_{1}^*}=1/3,\ {x_{2}^*}=3/2,\ {x_{3}^*}=3

    as written, these are not questions to be answered by definite integrals, as these are not Riemann sums.

    here you have n = 3, so you just want

    A \approx \sum_{n = 1}^3 f(x_k^*) \Delta x = \Delta x \sum_{n = 1}^3 f(x_k^*) = \frac 43 [f(x_1^*) + f(x_2^*) + f(x_3^*)] = \cdots

    and so on and so forth
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  3. #3
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    im not getting 71/6; im getting 94/9 can you see what im doing wrong
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by vinson24 View Post
    im not getting 71/6; im getting 46/9 can you see what im doing wrong
    x_1^* = \frac 43,~x_2^* = \frac 83,~\text{and }x_3^* = 4

    do you see why?

    do you get the answer now? what are you using for f(x)? the function you have at the end?
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  5. #5
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    i take each of those numbers and substitute them into x+1 and then take the sum of them and multiply the sum of those by 4/3 but i dont get the answer 71/6 also im getting 5/2 for x*2
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by vinson24 View Post
    i take each of those numbers and substitute them into x+1 and then take the sum of them and multiply the sum of those by 4/3 but i dont get the answer 71/6 also im getting 5/2 for x*2
    x_1 starts at 4/3 and you add 4/3 to that to get x_2 and then 4/3 to that to get x_3

    make sure you are looking in the right section for the answer. something seems amiss here.
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  7. #7
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    its the right section and thats the whole problem this problem is in the section of definite integrals
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