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 left-hand Riemann sum computed as $$2*1 + 2*6 + 3*10 = 44$$.
B
A midpoint sum approximation that incorrectly averages the endpoints without weighting by subinterval widths.
C
A right-hand Riemann sum computed as $$2*6 + 2*10 + 3*15 = 77$$.
D
A trapezoidal sum computed as $$0.5*(1+6)*2 + 0.5*(6+10)*2 + 0.5*(10+15)*3 = 60.5$$.
Question Leaderboard
| Rank | |||||
|---|---|---|---|---|---|
| #1 | vuphuonganh.150609 | 2 | 2 | 1m 22s | 118 |
| #2 | manyab1708 | 2 | 3 | 1m 16s | 114 |
| #3 | suhanakochhar006 | 1 | 1 | 0m 25s | 75 |
| #4 | 56369 | 1 | 1 | 0m 46s | 54 |
| #5 | Pelisx | 1 | 1 | 0m 49s | 51 |
| #6 | michellerar23 | 1 | 1 | 1m 13s | 27 |
| #7 | 26lmiller | 1 | 1 | 1m 22s | 18 |
| #8 | mouhamed.sall | 3 | 4 | 4m 34s | 16 |
| #9 | aurorachris0601 | 1 | 2 | 2m 18s | -48 |
| #10 | srinikasriyamathur | 5 | 5 | 56m 16s | -2,876 |
Items per page:
10
1 – 10 of 10