Unformatted text preview: 5 v ( t ) dt. Computing the two integrals on the right (do it!) gives 125 / 6 and17 / 6, and the sum of these is indeed 18. But what does that negative sign mean? It means precisely what you might think: it means that the object moves backwards. To get the total distance traveled we can add 125 / 6 + 17 / 6 = 71 / 3, the same answer we got before. Remember that we can also interpret an integral as measuring an area, but now we see that this too is a little more complicated that we have suspected. The area under the curve v ( t ) from 0 to 5 is given by Z 5 v ( t ) dt = 125 6 , and the “area” from 5 to 6 is Z 6 5 v ( t ) dt =17 6 ....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Addition, Derivative, .........

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