Unformatted text preview: applications of integrals that we have seen. It turns out that the identity is true no matter what c is, but it is easiest to think about the meaning when a ≤ c ≤ b . First, if f ( t ) represents a speed, then we know that the three integrals represent the distance traveled between time a and time b ; the distance traveled between time a and time c ; and the distance traveled between time c and time b . Clearly the sum of the latter two is equal to the ﬁrst of these. Second, if f ( t ) represents the height of a curve, the three integrals represent the area under the curve between a and b ; the area under the curve between a and c ; and the area under the curve between c and b . Again it is clear from the geometry that the ﬁrst is equal to the sum of the second and third....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Fundamental Theorem Of Calculus, dt

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