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I do not understand how to start this problem. I know I have to integrate from 0 to 1 and that n=3 but thats all. Hints/clues appreciated! enter image description here

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Do you know what a Riemann sum is? –  Nameless Nov 24 '12 at 18:55
    
i know n=3, i am confused at what the integrand is myself. –  gt2 Nov 24 '12 at 18:59
    
Is this your e-Homework sheet? Then you should add a homework tag to your question. –  Dominik Nov 24 '12 at 18:59
    
i added the HW tag. if anyone could just give me hints on what i should do to start the problem, it would be appreciated! –  gt2 Nov 24 '12 at 19:46
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1 Answer

Hint - Check the different sums given in (a)-(e), and take into account that:

== The function must be evaluated in points of the given subintervals $\,[x_i,x_{i+1}]\subset [0,1]\,$ , and way more important:

== Every value of the function must be multiplied by the correspoding subinterval's length!

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then only B would be the correct answer? –  gt2 Nov 24 '12 at 21:39
    
Yes, indeed (b). Can you explain why the $\,2\,$ before the first summand, though? Also observe that (c) almost makes it...what's the problem with it, though? –  DonAntonio Nov 24 '12 at 21:43
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