MA1014_HW3_201012

MA1014_HW3_201012 - Mathematics for Engineering II...

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

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

Unformatted text preview: Mathematics for Engineering II Homework 3: Integration by substitution. From your textbook (Thomas 11th Edition), section 5.5 5, 7, 9, 21, 27, 35, 39, and 45. From your textbook (Thomas 11th Edition), section 5.6 3 (both parts a and b), 11 (both parts a and b), 15, and 23 Total # of exercises: 14 3 4 5 Integration 8 Ê du œ $ 4 3 ˆ4 nswers 4 c 8‰ dx œ ' (sin u)A3 du‰ œ 3 ' sin u du œ x"Î$ dx Ê du œ x"Î$ dx 3 4 (ccos u) b C œ c 3 cos ˆx%Î$ c 8‰ b C 4 Section ˆv b 1 ‰ Ê du œ sec ˆv b 1 ‰ tan5.5b 1 ‰ dv # # # c1‰ # 5 tan ˆv b 1 ‰ dv œ ' du. œ u b C œ sec ˆv b 1 ‰ b C # # Ê du œ c csc ˆ v c 1 ‰ cot ˆ v c 1 ‰ dv Ê c2 du œ csc ˆ v c 1 ‰ cot ˆ v c 1 ‰ dv # # # # " # 7. 9. ot ˆ v c 1 ‰ dv œ ' c2 du œ c2u b C œ c2 csc ˆ v c 1 ‰ b C # # 21. " tœ' c# t b 1) Ê du œ c2 sin 7. b 1) dt Ê c " du œ sin (2t b 1) dt # 2 (2t du u œ " #u bCœ 35. # cos (2t b 1) 39. " bC n t Ê du œ cos t dt œ' 6 u du œ 6 ' uc$ 45. œ 6 Š u # ‹ b C œ c3(2 b sin t)c# b C du c 1 1 2 2 1 1 1 Ê du œ sec z tan z dz 1. a) , b) 6 2 " œ ' Èu du œ ' uc"Î# 5. 2 2u"Î# b C œ 2Èsec z b C du œ 3 1 € € 23. π / 3 œ tc" c 1 Ê du œ ctc# dt Ê cdu œ Section 5.6 Ê du œ ccsc# y dy Ê cdu œ csc# y dy "Î# , b) − y dy œ ' Èu (cdu) 3. c)' u"Î# du œ c 2 u$Î# b C œ c 2 (cot y)$Î# b C œ c 2 acot$ yb b C œa 3 3 3 1‰ dt œ ' (cos u)(cdu) œ c ' cos u du œ csin u b C œ csin ˆ " c 1‰ b C t € € € " t dt € 3œt "Î# b 3‰ dt œ ' (cos u)(2 du) œ 2 ' cos u du œ 2 sin u b C œ 2 sin ˆÈt b 3‰ b C " ) b 3 Ê du œ " c"Î# #t dt Ê 2 du œ " Èt dt Ê du œ ˆcos " ‰ ˆc )" ‰ d) Ê cdu œ ) " ) cos " ) " ) d) " " d) œ ' cu du œ c # u# b C œ c # sin# " ‹ #È ) bC " È) )œ' ) Ê du œ Šccsc È) cot È)‹ Š " È) cot È) csc È) d) œ ' c2 du œ c2u b C œ c2 csc È) b C œ c d) Ê c2 du œ cot È) csc È) d) 2 sin È) bC 5s b 5b a3s# b 4s c 5b ds œ ' u du œ s# c 5s b 5 Ê du œ a3s# b 4s c 5b ds u # bCœ as b 2s c 5s b 5b # bC ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online