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Math Help - What Do These Question Mean?

  1. #1
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    What Do These Question Mean?

    Through these problems, express the given limit as a definite integral over the indicated interval [a,b]. Assuming that [xi-1,x] denotes the ith subinterval of a subdivision of [a,b] into n subintervals, all with the same length Δx = (b-a/n, and that mi =1/2(xi-1 + xi is the midpoint of the ith subinterval.
    qqqqqqqqqqn
    qqqlimqqqqqΣ (x^3-3xi^2 +1) Δx over [0,3]
    qqqqn->∞qi=1

    qqqqqqqqqqn
    qqqlimqqqqqΣ (25-xi^2)^0.5 Δx over [0,5]
    qqqn->∞qqi=1

    Please show work and explain, I am very lost . Ignore the q's in the formulas.
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  2. #2
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    Have you heard of Riemann Sums?
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  3. #3
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    Wow. Maybe it's just my browser, but your "equations" are displaying as mostly long strings of the letter "q".
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  4. #4
    Member eXist's Avatar
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    Use Latex please: http://www.mathhelpforum.com/math-he...-tutorial.html

    I see a lot of q's and n's too
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  5. #5
    MHF Contributor

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    That's because most browsers do not respect "spaces" at beginnings of lines. In order to maintain the spacing, he put "q" at the beginnings of lines. Any way, LaTex is better. They are:

    \sum_{i= 1}^n (x^3-3x_i^2 +1) \Delta x over [0, 3]
    and
    \sum_{i+ 1}^n \sqrt{25- x_i^2} \Delta x over [0, 5]

    Billy Maize, obviously whoever gave you these problems expects you to know about the "Riemann sums" chengbin refers too. You can hardly expect a tutorial here but the basic idea is to divide the x-axis into a number of intervals, use the height of the function at each point to construct rectangles, then add the areas of the rectangle to approximate the integral.

    Taking the limit, as the number of intervals goes to infinity and \Delta x goes to 0, gives the exact integral. What you want to write for your answer is something like \int_a^b f(x) dx. Now what do you think a, b, and f(x) is for each of those? (I'll give you this hint- \Delta x becomes dx!)
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  6. #6
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    Thank you halls!
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