Question

Find an approximation of the area of the region R under the graph of the function f on the interval [0, 2]. Use n = 5 subintervals. Choose the representative points to be the midpoints of the subintervals. f (x) = x2 + 8

Answer 1

Trapazoidal's rule or SImpsons' rule?

Answer 2

you can use this to check your work http://nastyaccident.com/calculators/calculus/riemannMidpointRule

Answer 3

midpoint i don't think is trapezoid rule, but i could be wrong

Answer 4

Height Value:
Δx = (2 - 0)/5
Δx = 2/5
Δx = 0.4
Midpoint values plugged into the function:
(0.4) * ( f((0+0.4)/2)) + f((0.4+0.8)/2)) + f((0.8+1.2)/2)) + f((1.2+1.6)/2)) + f((1.6+2)/2)) )
Generated X values plugged into function:
(0.4) * ( f(0.2) + f(0.6) + f(1) + f(1.4) + f(1.8) )
Function values:
(0.4) * ( 8.04 + 8.36 + 9 + 9.96 + 11.24 )