Question

1. Evaluate the integral using FTC. -1/2 (a) d. d. (b) 5°2+ (c) [(4-2)(1 – 4) dt (a) Lisa (cos (e) – e=%) dt

Answer 1

Amaner 9,3 The du use the common integral S store dx = (aresinews] 12 compute the boundaries limatot (aresin (")) Faresin (0) peet и со (by common values) limnt 1/2 - Caresin (97) = aresin (7) put na 1/2 = 7 (by common values] 7 os]>

b> 2 tun du 4 expand and get tu 2 tu du 4 apply the sum rule 9 9 s 22 du + f F du 4 2 h du 4 = 2., h du 4 Commons integral I f du = ln (101) : 2 [ in 1122 compute the boundarica [mm112 limasa + (nimi)

put. n=4 = ln (4) = 2 10 (2) (by log reele) limuoa (losul) putreza Ilm (9) = 2 lm (3) (by log rule) » 211 (3) - 2 lm (2) = 2/2m (1) 2 In (29) The du apply radical rule at du 4 rant a le due (by expornut rule) 4 apply power rele n-12+1 -4+1 I 4

and get simplify = [25] 4 compute the boundaries limaat + - (200) put us 4 2 54 limusa (en) put naq = 259 6 >> 6-4 now, from above me e get = 2(21n (3) – 2 In 1299 +2

4 c.) (4-2) (4-4) at - expound and get H2-66f8 4 42-64 a 8 dd Apply sum/ difference nele 4 4 4 f t² dd - / 6A dd & J & dd -1 t2 dt apply power nele 4 +2+1 2+1 -1 compute the boundaries and get hellery 3 4 ے 6t at 4 = 6 1 4 dt *'[!]* (by (by po power rule

compute the boundaries and get 15 2 = 6, 15 2 - 6. = 45 4 به هر 8 da 19 [st] 1) fostegral of a constant compute the boundaries and get E 40 from above 11. alla 45 t 40 simplify and get - 50 3

12 d) (Cos (H)-e-ety at TA Apply sum rule 지고 cos(4) dt e-24 de TA I coa (A) dt TYA [sim (d)] / (by common postegral) T/A compute the boundaries and get I-te 1/2 e-24 dt 지사 apply ur Aubertitution U24 = feu (-2) de af - heu del

adjust fortegral boundaries. > u=-7 T daa » usat = np noe = - 7 -14- Ludu -(- 4 [eu]-*12 if ) by common fostegral simplify and get Ź[eu] - F/2 -T compute the boundaries and get station - e 11 2 lebilecek simplify and get 11 int e */2-1 2 en combine the fraction e 7/2 - 1 - - 2eX

/, 2 J2 ел t e 41 2 et