Use Simpson's Rule, the Midpoint Rule, and the Trapezoid Rule to estimate the value of the integral ∫3125f(x)dx.
In all cases, make n as large as possible, given that this table shows the only values of f that are known.
x 25 26 27 28 29 30 31
f(x) 2.6 2.6 2.5 2.8 3.7 3.8 4.1

Simpson's Rule approximation Sn=
Midpoint Rule approximation Mn=
Trapezoid Rule approximation Tn=

Question

Use Simpson's Rule, the Midpoint Rule, and the Trapezoid Rule to estimate the value of the integral ∫3125f(x)dx.
In all cases, make n as large as possible, given that this table shows the only values of f that are known.
x	25	26	27	28	29	30	31
f(x)	2.6	2.6	2.5	2.8	3.7	3.8	4.1

Simpson's Rule approximation Sn=
Midpoint Rule approximation Mn=
Trapezoid Rule approximation Tn=