Question

Evaluate the Riemann sum for f(x) = x2 + 2x – 1, 1<x< 4 with six subintervals, taking the sample points to be right endpoints.

Answer 1

F(x) = x?+23-1 I ens 4 na 6 intervals Right end points for Right int end point sum. I. Fuldn AL Fr(ka) + F(m2) + - +Front) +F (an?] where An b-a h. we have that a21 b = 4 na 6 > Ax z 4-1 6 الم 2 interval [1,4] into nao subintervals 2 Divide the of legn A2 = 1 113 37 3 2 2 > 5 2 Hl 2 S 2 2 a= -> 2 2 1 4 ab 7 2 the the function at 71737 + -Now we just evalvak endpoin' FCX,) = f(1) 17 4.25 11 12+ 2(2)-1 7 Fra12) F(2) K (M3) = F() - ()*+ e[])-+= st. 2.10.25

f (xg2 F13) 02?+2(3) - 1 2 14 - Flas) ] (3)+2(2) - 573 18.5 AR frao) F (4) 7(4) = +4 ()2+265)-1 = 23 Riemann sum [F(*12+ .f(22) + f (23) + Flame) + F(45) +6222)] Į (Gress +7 + 10.25 +16+ 18.25+23 P 2 Ler 38.375 1 Riemann sum for Fir) = 22 + 2x - ) is 38.375

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