Integ_tut_sol1

Integ_tut_sol1 - Integration I Solutions to Integration I...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Integration I Solutions to Integration I Exercises 1. a) 4 7 3 3 3 x dx x C 7 = + b) 2 1 2 3 3 dx 3 x dx 3x C C x x-- = = - + = - + c) ( 29 2 3 2 2 1 1 x x dx x x 2 dx x 2x C x 3-- + = + + =- + + 2. a) ( 29 3 2 3 2 2 1 2 1 1 2 d 2 d 2 C 2 1 1 2 C 2---- +- = + - = -- - + = --- + b) ( 29 2 1 2 3 3 2 3 4 ax bx c dx ax bx cx dx x a b c x x x C 2 3 4--- + + = + + = + + + 3. a) ( 29 2 2 2 2 2 4 1 1 2 3 1 1 2 x 1 d x x 2 x d x x x 2 x 2 8 1 1 2 3 3 8 3 1 6 3 4 3-- - = - = + = +- + +- - = = 3 4 3 6 1 3 8 2 3 1 1 3 8 x 2 3 x 2 1 1 3 =-- + = +- + = + =- b) ( 29 ( 29 ( 29 ( 29 [ ] 4 4 2 4 3 2 4 4 3 2 x x 1 x 2 dx x x 3x 2 dx x 3x 2x dx x x x 4 64 64 16 16-- =- + =- + =- + =- + = 4. 1 Integration I ( 29 ( 29 ( 29 2 2 2 2 2 2 2 2 2 1 dy 1 x 1 dx dy 1 dx 1 x dx y 1 x Let x tan 1 x 1 tan sec and dx sec d sec y d sec y d C tan x C- + = = + = + = + = + = = = = = + = + 5. ( 29 2 2 dy 2x 1 dx y 2x 1 dx y x x C when x 1 and y 1 1 1 1 C C 1 y x x 1 =- =- =- + = = = - + = =- + 6. 2 2 2 1 3 2 1 2 d x 2 3t (acceleration) dt dx 3 2t t C (velocity) dt 2 t x t C t C (distance) 2 = + = + + = + + + when t = 0 x = 5 5 = 0 + 0 + 0 + C 2 C 2 = 5 When t = 1 dx 10 dt = 2 Integration I 1 1 3 2 3 10 2 C 2 13 C 2 t 13t x t 5 2 2 When t 1 1 13 x 1 5 2 2 x 13 = + + = = + + + = = + + + = 7. a) ( 29 ( 29 ( 29 3 3 3 4 4 Evaluate 2 x dx Let 2 x u dx du 2 x dx u du u C 4 1 2 x C 4-- =- = - = - = - + = -- + b) ( 29 ( 29 ( 29 ( 29 3 3 3 2 2 E valu ate 2 x 1 d x L et 2 x 1 u 2 dx d u 1 2 x 1 d x u d u 2 u C 4 1 2 x 1 C 4 1 C 4 2 x 1------- = = - = = - + = - - + = - +- = 2 ) 1 x 2 ( 4 1- + C 3 Integration I c) 1 2 1 2 dx Evaluate 5x 7 Let 5x 7 u 5dx du dx 1 u du 5 5x 7 2 u C 5 2 5x 7 C 5--- = = =- = + =- + d) ( 29 ( 29 ( 29 2 2 2 Evaluate sec 2x 1 dx Let 2x 1 u 2dx du 1 sec 2x 1 dx sec u du 2 1 tan u C 2 1 tan 2x 1 C 2-- = = - = = + =- + 8. a) Evaluate - d 2 3 sin 6 / Let - 2 3 = u, when = 0, u = 3 2d = du = 6 , u = 3 3 = 0 [ ] 6 6 3 3 3 E v a lu a t e s i n 2 d 3 L e t 2 u w h e n 0 u 3 3 2 d d u u 0 6 3 3 1 s i n 2 d s i n u d u 3 2 1 s in u d u 2 1 c o s u 2 1 1 1 2 2 1 4 - - = = = - = = = - = - = - = = - = - - = 4 Integration I b) Evaluate + = + 3 / 2 2 3 / 2 2 u 4 9 1 du 4 1 u 9 4 du Let 4 9 u 2 = tan 2 , when u = 0, = 0 2 3 u = tan u = 3 2 , tan = 1 [ ] 2 3 2 3 2 2 2 2 2 2 3 4 2 2 2 4 2 2 4 4 d u 1 d u E v a lu a te...
View Full Document

This note was uploaded on 04/25/2010 for the course MATH 201 taught by Professor Any during the Spring '10 term at Westminster UT.

Page1 / 19

Integ_tut_sol1 - Integration I Solutions to Integration I...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online