


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
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
mat 129 exam 1 fa24. notations
Typology: Exams
Uploaded on 01/29/2025
1 / 4
This page cannot be seen from the preview
Don't miss anything!
Math 129 Exam 1 Fall 2024 Name (Please Print.): 8 points each You need to show all your work to get a full credit. sin^2 1 cos^2 , cos^2 1 sin^2 , sec^2 tan^2 1, tan^2 sec^2 1, sin^2 1 cos 2 2 , cos^2 1 cos 2 2 , sin 2 2 sin cos , sin u cos v 12 sin u v sin u v , sin u sin v 12 cos u v cos u v Problem 1 Evaluate each integral.
Cheawon kim = (^) ( (" (^) )- Se"ds^ = e" sC = xe
da =^ x^ - (entc)
2 = SEoseEu 38 dy ∅ U =^8 c = S cos^4 ]^ du duz 8 dc^ U 2 = (^) Ih dy=^ dx. = ☆ S cos^4 Eu) du =^ →^ duz^ =dn ⑤ Sco(u)^ ) ' du daz=^ du = δ fl (^ tcos ?]e du. @.^ (+^ by]^ = (olastctScoscusl du,) +^ f (^4) durtfssand
( (^) tc 0 s) " ' a(
l(aHsn =^ )catans
]
= aztzabtakb^2 = (^6) ( ( ust + (^) ( sin( us)tc )]t * (^) μ 2 + C +fcosdanc) = oS [ π (^4 4) t s)+ JIosCuz )dus ( )
: (^) (
..^.
omiaur+ 5 .) -^ (^ +δ^
= (^) ( o^3 tin (u) .tsin) +^ c
③ +in( s 6 +^ sin(^16 tC .. )) .
)
U
x^2 x 2 dx
U 1 =^ x-^2 Ua =^ at^1 dul =^ dss^ duz = (^) bl. = (^2) S = x- (^22) J ( - 2 )-
()dx =^2 (^ S (^) - sdctSx^ ←^ ")dx ) = (^2) (* 5 -^ dbu+^5 - +Ddc
Sa,^ du^ +^ S - (+ *) da )^ = 2 (^ (^ n…^ (^ m^ ))^ +^ c? - ( (^) ) .)) = =^ [ (n^ (^ ui^ ))-^ (^3) S du. ) = (^2) (( In lul) +c) - ( inluajtc) = (^2) ( | (|) - In(^ lul))^ +^ c = (^2) CU(|^ )-^ ⑤ u =^ Eos^ (ax) dureaa = Scosx e^ " dx =^ (os (x) e ". Soctsin (xy^ )dc = cos (a)e Ife
= (^) cosoc) e^ " t
ex ds^ u= sin EsC) dr =^ ex e " cos (a)^ dx^ = (^) cos (sa) extsina )ea^ = Sercosa)ds = rcosa^ )^ e'^4 sinxer : sue
Gpr
Problem 2 Write the partial fraction decomposition but do not finish the computation. 3 x 5 x 8 ^3 x^2 x 2 Problem 3 Find the following integral by the trigonometric substitution
=
∞ ) .
since x=^ sin^ (ω) (^) , - W^ Then (^) , dac = Cos tw)^ theefore (^) cos(o)ispositive.
= ( Sdwt (^) Scos (aw)^ dw> a =^2 w
:
dl= 2 dw Idu =^ dw = (W^ +^ c^ +^ S cos (^) la). *du (^) )
o sarcsimb)
= Larcsin (oc) + (^) (s ))tC
=^ arcsi tin (^2 arcsina +^ c = aresinca) t