How do you find the Riemann sum for #f(x) = x - 5 sin 2x# over 0 <x <3 with six terms, taking the sample points to be right endpoints?

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Answer 1 · 2015-05-15T16:09:15

#f(x)=x-5sin2x#, #a=0#, #b=3#, #n=6#

Apply the formulas (the ideas).

Cut the interval #[0,3]# into six equal pieces. Each has length
#Delta x = (b-a)/n = (3-0)/6 = 1/2#

Starting at #0# (the leftmost left endpoint), find the right endpoints by successive addition of #Deltax# (the length of the subintervals):

#0+1/2 = 1/2# is the first right endoint

#1/2+1/2 = 1# is the second right endoint

and so on to get:

#1/2, 1, 3/2, 2, 5/2, 3# are the right endpoints.

The Riemann sume is built by finding #f# at the endpoint times #Delta x# and adding:

#f(1/2)*1/2+f(1)*1/2+f(3/2)*1/2+f(2)*1/2+f(5/2)*1/2+f(3)*1/2#

Now do the arithmetic. (You'll either need a calculator or you'll need to accept your answer with sin(1), sin(2), sin(3) etc. in it.)