Unformatted text preview: missing is Δ t —but in fact, Δ t = 1 /n , the length of each subinterval. So rewriting again: n1 X i =0 sin( πt i ) 1 n = n1 X i =0 sin( πt i )Δ t. Now this has exactly the right form, so that in the limit we get average speed = Z 1 sin( πt ) dt =cos( πt ) π ﬂ ﬂ ﬂ ﬂ 1 =cos( π ) π + cos(0) π = 2 π ≈ . 6366 ≈ . 64 . It’s not entirely obvious from this one simple example how to compute such an average in general. Let’s look at a somewhat more complicated case. Suppose that the velocity of an object is 16 t 2 + 5 feet per second. What is the average velocity between t = 1 and t = 3? Again we set up an approximation to the average: 1 n n1 X i =0 16 t 2 i + 5 ,...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Approximation, Velocity, Sin

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