{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT18_014F10_pset2

# MIT18_014F10_pset2 - If not well-deFned provide a...

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

Unit 2: The Integral Pset 2 Due September 24 (4 points each) (1) page 57: 9de (You may use 9abc as you already proved those for recitation) (2) page 60: 6 (3) page 70: 7 (4) page 70: 11ac (5) Prove, using properties of the integral, that for a, b > 0 a 1 b 1 ab 1 dx + dx = dx. 1 x 1 x 1 x Define a function f ( w ) = w 1 dx , for w R + . Rewrite the equation above 1 x in terms of the function f . Give an example of a function that has the same property as the one displayed here by f . (6) Suppose we define b s ( x ) dx = s k ( x k 1 x k ) 2 for a step function s ( x ) a with partition P = { x 0 , x 1 , . . . , x n } . Is this integral well-defined? That is, will the value of the integral be independent of the choice of partition? (If well-defined, prove

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: If not well-deFned, provide a counterexample.) Bonus: DeFne the function (where n is in the positive integers) f ( x ) = x : x = 1 1 2 n : x = n 2 1 Prove that f is integrable on [0 , 1] and that f ( x ) dx = 0. 1 MIT OpenCourseWare http://ocw.mit.edu 18.014 Calculus with Theory Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

MIT18_014F10_pset2 - If not well-deFned provide 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