This document contains the step-by-step working of an integral calculation. It begins with an integral of the form ∫(x^2 - 8x + 12)dx from 0 to 2. Through successive substitutions and integrations, it arrives at the solution of -16.

1. i-
flr
.4{^
tf)"'
L . lu (*+q)a*
-[i o^il:
- lLe l'* i(,B ) ro
-'3+ 3z --f.1 sq.{rqa.( Lucts
=,lo Lx) dx -h f { (") dvu-2 (Jo
z l-*'Jl, + i^3J
=Ztlt"r !t."t") tic.l- *o)3
;:-t8
= [O Sat{a1r (rtas
q . Y'Y-' , Sumbu r &ct X=r I *frl a
t =J' Lx" ) d*
t:r)Z
= g 9ct*rrqn tr-AS
b' I =xt-8x*tz J.an sqrnbq x
/ o=, , b=-8. c=t2
D , bL* tqq
=!8J'- I Cr )(tzS
=t6
xa^8xrt2"o
tx-a) tx-z) --o
*-L, x>2
t +rt
. lu..c.ar L-b/oo ,o /_^o) , Lq ,-1 )
=-J' x'-8xttz dx2
= - [ta
x2 - 4r' +.r.^JJ:
=l(iLq,*qG)'t L L(Lr- ( I L4'^ rttp)u+ trt41j
3G
! x'J 1,
czsv -
I a '(.
= 9-333
Ecx) 'Y