Question

11. Use the definition of area under a curve (this means the long way with sigma) to find the area Port under f(x) = x2 - x on the interval (2, 3). U zielone world be brio trilogroll be bivog brat mora s obytu nismo 21993 vishda methe lo bro

Answer 1

11) Ciren fox) = x-x [2,3] Area under corre foo over [a, b] interval notation using Syma Ib Fooda = lim { no i=1 f(a). Da where Da = b-a 2i = at Here a=2, b=3 FGC) = x²_x Da = b-a n Da = 3-2 on If Dxn 2 4+02 n Area under corre 3 2 (x²-x) dx (a2-x) dx = lim +82 +49 2 + پالک (4+ 4 + 2 + 43 n2 - Lim 2 + 02 + 3.) + 2 + 92 n3 +39 n = lim + lim 3 (2 no 9-1 2 we know that som of n natural nombers us non) Som of squares of is natural numbers is ED nt (2) (21) .

lim nCnt) 12 2 lim 6 n3 lim + in3 (1+h) (2+1) 7 . 13 n2 (on the chal Cant to > ( non(+1) n (2+2 +3 [20 (th) [2+ + CH (2+1) + 3 CHI) As nodot no [24 2+ + (1+0) (2 to) [2+ + (2) + 3 2 CD] = 2 + 1 2 + 33 11 lim + 12 +2+9 6 23 6 23 ( (12_x) dx