Page 83 - Math Grade 12 (Advance)

PROEUS DARA
'ijjltJ t ~tJ rali mtl L\ v r:ll'i:ll~ tiJ rn &lL&l1stl L\x nrn L\ v tn s &l ~~ t m m ff1 g ~ £Ultl 'Lni
u

2 L\v 2
n[f(x)] ::;; L\x=:;n[j(x+L\x)]
2 2
mrnrun L\x--70 &Sl8 lim n[f(x+L\x)] = rr[f(x)]
t.x->0
2 2
tlmsg lim ~:. = n[f(x)] 'i5 V' = n[f(x)]
u l'.x-70 L.U "'-
2 2
V' = n[f(x)] tnssrum V dlUl~g~~s rr[f(x)J
2
ttl F(x) mw~g1~ti5~S rr[j(.x)] &Slg V = F(x) + c , c E IR thmg .x = a
""
V = 0 tlil ti5 0 = F(a) + c , c = -F(a)
tlmsg V = F(x)--F(a)
u
2
tti X fLTIUJbli~ a &9'4 b tf:'!LilS v = F(b)- F(a) = n r [f(.x)] dx '1
w a

~ f' "
nblfl&Hi::!lti5 V = lim L.J n[f(xk)] L\.x = n [f(x)rdx '1
2
'
0
11 ~+ oo a
k=l
y
RM~r:ns~sf1rnil1miin~ x'ox ~s~drtlrn2Mti::!lti5
.J I ~ U ~ ~
LAl'i5&ntlH9f:'l'ijS y = i StlHRJHlth~M ttflti5UlJ
u

X

x' ox '01 S tl tH ff1 g l 0, I ] R blil ~ t i::!l ti5
u
1 J 1 1 1
n
2
J 5
2 z J 4
V = n [f(x)] dx = n (x) dx = n x dx = n [ 1 s] = :S tln&n'ifl~ '1
x
0 0 0 0
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