Question

1. (10 pts.) Compute the following integrals (a) [ 10 de In clos to (1) londo (a) seeds (bonus) 3+2V2)r? - 2x +3 dr (Hint: +1-(-x+ 2r - 1)(x - 2x - 1))

Answer 1

o) Consider the intagral S1 d 1 C log0o Cb) ConsideY t2e tntegrol sece -secO Tanot Bubshitule TOno then 17 cund da sece.do TouYO sec de Seco de sece Seeco-) Seco de -secče - seco) de 17 Ssecode-secodo secco).TOne Ssecode -Sseco de 2 seco. TanG -Ssecodo 2 2. Seco TanO -In(sece+Tano)+c In CR4 ) C 2 2 +C 2 2

c) Consider the integra = xp ba S Substitaue a 3 sece thon da -3seco TOn@de e rp b-x s J9sec'e faseeo 9 39eco Tano do 9 Sec'e 3 TCune 3Tane seco d9 1 Sseco.Tano de 3 - 81 S secoC sec'o -) de SCseco-seeo) de Seeco do do seco do - Seeodo Seco Tan 3 4 81 4 Seco Lop *울Jseccdo이 ,Tono 81 - 81 sece. Tane- 8 4 Seco TOnG 4 81 secs. ·횡In1seco+TonotC Tono- Seco Tang 4 32 3 -9 C ( b

integral (d) consideY the Sare da 201 Csing inagration by poos fomula 22 221 da ae 2 2 4 2 Ce) consi'der the inte gral 2 dx Cr-3)at3) 2 3+2 Let fr) (a-3)a13) Then fa So that f s an odd function. -Use the property of inkgra 2 fa)da if fa) iseven fa)da D , if fa) %odd 2 2 da =0. cue have (A-3)CA3) 2