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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 sub-intervals (not all the same size). Estimate the function f by another function g which is constant on each of these sub-intervals. That is pick an actual constant value for each sub-interval which you think best represents f on that sub-interval. c) Find the average value of g on the interval [0 , 4]. (Hint: On any sub-interval, 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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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
- Spring '08
- Fundamental Theorem Of Calculus