1. ## Trapezoid Methods

First Question:
Using the trapezoid method, approximate the area under f(x) on [0,8] to the nearest integer given the following:

x | 0 | 1 | 2 | 3 | 5 | 7 | 8 |
f (x) | 3.4 | 2.7 | 6.2 | 5.3 | 1.3 | 2.1 | 4.8 |

I know the trapezoid rule is :

but I'm not given the whole f(x) values from 0 to 8. for the area of the trapezoid would it be 8-0 / 16 = 1/2 ? and for the inside how am I supposed to calculate f(4) and f(6)?

Second Question:

Below is a table for f(x). Find the positive difference in calculating 1∫13 f(x) dx by using 6 left rectangles and 6 trapezoids.

x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
f(x) | 0 | 3 | 5 | 6 | 7 | 8 | 10 |12 | 16| 18 | 20 | 21 | 23 |

For the 6 left rectangles I use 1 - 6? but how about the 6 trapezoids? which domain am I supposed to do it from? 7 - 12?

2. the "packaged" trapezoid formula does not work for a set of data with unequal base lengths.

you'll need to find the area for 6 trapezoids ... 4 of them have a $\Delta x$ length of 1 and the other 2 have a $\Delta x$ length of 2.

for your second question, $\Delta x$ = 2 , not 1.

3. ok so I got 26.7 for the first question. but I still don't get the second one. I just use the left hand sum for first 6 x values? then I don't know what to do for the 6 trapezoids