Question

please simplify

Problem 2.3 Evaluate or simplify the following integrals or expression as much as possible (show your work). (a) L, 8(t)x(t – 1)dt (e) , 8(at)dt (i) cos(10zt) [8(t) + 8(t + 5)] sin (b) 8(t – T)x(t)dt (f) 8(2t – 5) sin nt dt (c) L 8(t)x(r – t)dt cos (x - 5)|6(x – 3)dx (sin ke (B) e*-2 8(w) (k) 6(r – t)x(t)dt (d) (h) Jt-11 t+9 8(1 – 3)đr

Problem 2.3 Evaluate or simplify the following integrals or expression as much as possible (show your work). (a) L, 8(t)x(t – 1)dt (e) , 8(at)dt (i) cos(10zt) [8(t) + 8(t + 5)] sin (b) 8(t – T)x(t)dt (f) 8(2t – 5) sin nt dt (c) L 8(t)x(r – t)dt cos (x - 5)|6(x – 3)dx (sin ke (B) e*-2 8(w) (k) 6(r – t)x(t)dt (d) (h) Jt-11 t+9 8(1 – 3)đr

Answer 1

It) (t-1) di • S(t) = 1 to 1 cu tto Toxt-aldt + J-1.xft-T) di . X(t-?)dł Ох Eotaro-T) to o xon 3 t-T) x (t) at SS(+-^) = 1 at tar co else O&st. RH dt (1) 2 = z 9 Í S4 x (x++) at

= of St. 2 (7-E) dt to X() Exam as j SCP-t) « Et at (T-t) & (t) dt make sure that Į slo) = 1 ( ) Eo otherwise = 0 + ll. x (t) at T-tal at t=ł = X(T) os į seen at S (at) = 1 SIH 19 - di Scat de 8478 ४ 7o St) dt = á x1 to to -

+) js(atuscinit at +s€(4-3) samt at (9) S 4-7) Sovt at I JE-S) in itat inttdt (at test s 514-5)/ zo else = 4x Sin TCE) £ sin 8 x 180° * ¢ sin (to) 두 - 수

02-2 cos E (-s) | 5 (-3) dx - SS (R-3) = 1 at n=3 Se cos 11 (t)) du l to elise Eot l pa cos To else 3 -2 se cos (3-5) • •' (4 xem ze cosa sex f-1) =-e T zei S(1-3) dr S(-3) = 1 at 9a3 - Eo else (tall to T=3 iton) lies in the limit T-11 to ľ+q

Therefore Ans=5 (3-31 E sro y Cos (100+) [5(4) + S (4+5)] c cos (2017) SW f cos (1077) 5(+5) = cos (lonxo) + Cos (oTx-s) = Cos (0)+ Cos FSOTT) 3 1+1 is sint st) +²t sino 0241 SEI) = 1 at t=0 zo else

- Sino) ON k) (sin Kw) Sw) S(W) = at wro = senkio) zo else cos Is in determinate form 23 Apply & hospital rule È a w Eink w) W -D cos(k wlX K Wzo = K Cos (0) (Oslo) =)