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Area summation problem under a curve

  1. Apr 8, 2017 #1
    1. The problem statement, all variables and given/known data
    Snap2.jpg
    Why, in:
    $$\frac{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}{n^{3/2}}$$
    There is ##~n^{3/2}## in the denominator?

    2. Relevant equations
    Snap2.jpg

    3. The attempt at a solution
    it should be:
    $$S_n=\sqrt{c_1}\Delta x+\sqrt{c_2}\Delta x+...=\Delta x\cdot \sqrt{\Delta x}+\Delta x\cdot \sqrt{2\Delta x}+...=\sqrt{\Delta x}\cdot \Delta x(\sqrt{1}+\sqrt{2}+...+\sqrt{n})$$
     
  2. jcsd
  3. Apr 8, 2017 #2

    fresh_42

    Staff: Mentor

    It should be ##\sum_k f(c_k) \Delta x##. Now ##c_k=k \cdot \Delta x\, , \,f(c_k)=\sqrt{c_k}## and ## \Delta x=\frac{1}{n}##. You simply stopped too soon before substituting ## \Delta x=\frac{1}{n}##.
     
  4. Apr 9, 2017 #3
    Thank you fresh_42
     
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