RandolphT2W98

RandolphT2W98 - improper integral converges or diverges ....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Winter 1992 Math 21 Test #2 Name 1. (10 points each) Find only FIVE of the following six indefinite integrals. Show each step. Circle the integral for problem that you DO NOT want to be graded . ( This will be graded on an all-or-nothing basis for 4 points extra credit.) (a) Z cos(3 x ) cos(4 x ) dx (b) Z x - 3 x 2 +1 dx (c) Z 1 4 x 2 +1 dx (d) Z tan 3 xdx (e) Z x 2 ln xdx (f) Z p 9 - x 2 dx 2. (10) Use partial fractions to express the integral as a sum of simpler integrals. Z 5 x 2 +3 x - 2 x 2 ( x +2) dx DO NOT EVALUATE the integral. 3. (a) (4 pts) Use the trapezoid rule with n = 4 to approximate Z 1 0 e - x 2 dx . (b) (6 pts) If T 4 is the number you found in (a), how large is the difference: Z 1 0 e - x 2 dx - T 4 ? You may use the fact that for f ( x )= e - x 2 , f 00 ( x ) 2 for x [0 , 1]. (c) (6 pts) How large should n be in order for the trapezoid rule to produce a value, T n , that approxi- mates R 1 0 e - x 2 dx to within 0.001? 4. (6 pts) A definite integral has been calculated for you below. Determine whether the corresponding
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: improper integral converges or diverges . If it converges, specify its value. Z t 1 ln x x 2 dx = ( using parts ) =-ln t t-1 t + 1. Therefore, Z 1 ln x x 2 dx = 5. (10) Show all your work in determining the value (if it exists) of the following improper integral. If it diverges show your work in determining this. Z 3 2 3 x-2 dx 6. (8) Use the comparison thoerem, explaining how it applies, to determine whether the integral is convergent or divergent . You DO NOT need to evaluate the integral. (You may use, without proof, any knowledge about convergence or divergence of the improper integrals involving 1 /x , 1 /x 2 , e-x , etc., but be specic.) Z 1 sin 2 x x 2 dx...
View Full Document

This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.

Ask a homework question - tutors are online