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Unformatted text preview: WORKSHEET 31 Fall 1995 1. a) Give the definition of a definite integral. b) State the Fundamental Theorem of Calculus. c) What is wrong with the following argument? Z 2 1 dt t 2 = − 1 t 2 1 = − 1 2 − − 1 − 1 = − 1 2 − 1 = − 3 2 2) a) Let f ( x ) = 4 x − x 2 . Draw a graph of this function on the interval [0 , 4]. b) Partition the interval [0 , 4] into eight subintervals (not all the same size). Estimate the function f by another function g which is constant on each of these subintervals. That is pick an actual constant value for each subinterval which you think best represents f on that subinterval. c) Find the average value of g on the interval [0 , 4]. (Hint: On any subinterval, g is constant  so there it’s average value is that constant. Now what fraction of the whole interval does each subinterval take up? How do you need to use this information in your computation?) d) We define the average value of f on the interval [ a, b ] to be y ave = 1 b − a Z b...
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 Spring '08
 Grether
 Calculus, Derivative, Fundamental Theorem Of Calculus

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