Question

2. Determine the following integrals, giving exact values for the definite integrals (and simplify as much as possible!). (4 points each) x-&x a) x se -cos(x) + 2" Jdus b) ſxvx-1dx The Adventure Continues e) [r? n(x) dx

Answer 1

0-2 (a) x x dut Se -DX ital dx-fcos(nisu + [2442 x I= It Is t Iztly 1,5 s 2 2 zda Iex² put Itu ² = ta zadre=dt ndx=dt at I, = s de 2 t Ij = 1 log (t) = 1, 1/2 log (1+x²) I, - X du 23 TE Flex's-xs de 2. = {( x - **) dx [:{x" dx = yhtl 2 = x3+1 43+1 I, = 3x3 + 7 5 7 1, - -|CSCM) ** - Cos (1) Iz -

Ey = /2² de (sar dua x а ina x Iy 2 in 2 so ws 7 I = I log (1+x) + 3 x 68 2 -x lost t x to in (2) 2 5 7 A ។ x Ju-l u-l du -1 =) dx = at x=-1, t = -2 x = 4, t = 3 B) S put x-1=t x= (t+1) S (t+1) St at I (+²24 +²2) at 3 -2 3 2 an 34+1 + [ + 3 + 1 ķt - 2 32 petite + 2t? 5 3 -2 2 (3) 21-2/2 26-23² + 3 5 3 28 13 222 A 5

e) sx en (4") du [By Past's integrate] ) - SP xen (x" ) - † = x ln("") 3 xdu 3 3 & ln (*") - 2 + CA 3 6 Juces ucx) dx = UK) Sucude (1 duo queda de