# ws31 - WORKSHEET 31 Fall 1995 1 a Give the definition of a...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

ws31 - WORKSHEET 31 Fall 1995 1 a Give the definition of a...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online