well, just looking at the rightmost term where x = 2
we have sin (1/2)
so I believe that you are correct and the teacher wrote sin( x ) instead of sin (1/x).
Use a Riemann sum with n = 3 terms and the right endpoint rule to approx. ∫(1, 2) sin(1/x)dx.
My teacher just needs the terms written out, no need to add or multiply. This is a problem she did up on the board, so here's her answer:
sin(4/3)(1/3) + sin(5/3)(1/3) + sin(2)(1/3)
I might have misread her writing, but is this right? Wouldn't the (1/x) in sin(1/x) create:
sin(3/4)(1/3) + sin(3/5)(1/3) + sin(1/2)(1/3)
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