The speed of an airplane was recorded every five minutes...

The speed of an airplane was recorded every five minutes during the first 40 minutes of its journey (see table below). Use the trapezoidal rule to estimate the total distance travelled by the airplane during these 40 minutes. time (minutes) | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 speed (km/hour) | 0 | 171 | 207 | 243 | 270 | 292 | 308 | 315 | 320

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0:00 Talk about this question.

00:01 We are given the tabular information about the speed and time and we need to find a total distance which is traveled in these 40 minutes using the trapezoidal rule.

00:12 So we know that in the graph of speed versus time, the area under the curve gives the distance and the area is given by the integration.

00:20 So that integration we have to find using the trapezoidal rule.

00:24 So first things first we need to find delta x which is going to be b minus a or the number of intervals.

00:31 So that's going to be the b is the highest value.

00:38 So that's going to be a b.

00:40 Whenever we'll graph it, we'll have the time on the x -axis and the speed on the y -axis.

00:47 So the t is actually the x coordinate.

00:49 So that's going to be 40 minus 0 over 2.

00:52 So that's going to be 20.

00:54 This is the data x.

00:56 And now we have to find the area.

00:59 So the formula for the area is going to be delta x over two or let's call it distance distance using the trapezoidal rule is going to be delta x over two then we have we have to write all the functional values but in a specific way so the first one is going to be f of x not x not is the first element plus plus two times the rest of the rest of the functional values and the last functional value is written over here.

01:38 So this is what we have to find.

01:40 So everything is actually given...

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