Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Material Type: Assignment; Professor: Bertrand; Class: Analysis I; Subject: MATHEMATICS; University: University of Wisconsin - Madison; Term: Spring 2009;
Typology: Assignments
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Homework 11
Exercise 1 Do the exercise 8 of the Chapter 6 of the textbook. Hint: use the partition Pn = { 0 , 1 , 2 , · · · , n}.
Exercise 2 (1) Prove that
1
1 xα^ dx^ makes sense if and only if^ α >^1. (2) Prove that
0
1 xα^ dx^ makes sense if and only if^ α <^1. (3) Compute
∫ (^) i 1 nf ty^
1 x^2 dx^ and prove that^
n^2 <^2. Prove that
Exercise 3 Prove that
∫ (^5) π 0
sin t 2+cos t dt^ = log 3.^ Hint: use the change of variables^ s^ = cos^ t.
Exercise 4 Compute
0 cos
(^4) tdt.
1
