APFIVE Trapezoidal Sum Approximation From a Table
The table above gives values for a function $f$ at selected values of $x$. Which of the following represents the trapezoidal sum approximation for the area under the graph of $f$ from $x=0$ to $x=7$?
| x | 0 | 2 | 4 | 7 |
|---|---|---|---|---|
| f(x) | 1 | 6 | 10 | 15 |
A
A trapezoidal sum computed as $$0.5*(1+6)*2 + 0.5*(6+10)*2 + 0.5*(10+15)*3 = 60.5$$.
B
A left-hand Riemann sum computed as $$2*1 + 2*6 + 3*10 = 44$$.
C
A right-hand Riemann sum computed as $$2*6 + 2*10 + 3*15 = 77$$.
D
A midpoint sum approximation that incorrectly averages the endpoints without weighting by subinterval widths.
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