اﻟــــــﺪوال اﻷﺻـﻠﻴـــــﺔ -1ﺗﻌﺮﻳـــﻒ : ﻟﺘﻜﻦ fداﻟﺔ ﻋﺪدﻳﺔ ﻣﻌﺮﻓﺔ ﻋﻠﻰ ﻣﺠﺎل . Iﻧﻘﻮل أن اﻟﺪاﻟﺔ Fداﻟﺔ أﺻﻠﻴﺔ ﻟﻠﺪاﻟﺔ fﻋﻠﻰ Iإذا وﻓﻘﻂ إذا آﺎن : Fداﻟﺔ ﻗﺎﺑﻠﺔ ﻟﻼﺷﺘﻘﺎق ﻋﻠﻰ اﻟﻤﺠﺎل . I )F '( x) = f ( x وﻟﻜﻞ xﻣﻦ : I ﻣﺜــــﺎل : -1ﻟﺘﻜﻦ إذن :
F ( x ) = x2 + x + 1 F '( x) = 2 x + 1
إذن :اﻟﺪاﻟﺔ Fهﻲ داﻟﺔ أﺻﻠﻴﺔ ﻟﻠﺪاﻟﺔ fاﻟﻤﻌﺮﻓﺔ ﺑــ :
f ( x) = 2 x + 1
-2ﺣﺪد داﻟﺔ أﺻﻠﻴﺔ ﻟﻜﻞ داﻟﺔ ﻣﻦ اﻟﺪوال اﻟﺘﺎﻟﻴﺔ : f ( x) = 2 -a
\ ∈ F ( x) = 2 x + C / C -b
f ( x) = x 1 2 x + C 2
-c
f ( x ) = x3 1 4 x + C 4
-d
= )F ( x
= )F ( x
*` ∈ / n
f ( x ) = xn
1 x n +1 + C n +1
= )F ( x
-e
}f ( x ) = x r ; r ∈ `* − {−1
-f
1 x r +1 + C r +1 f ( x) = x
= )F ( x
1
= x2 2 32 x + Cte 3 -g
)(2 x + Cte
3
)+ 1 4
= )F ( x 2
(x
)+ 1
1 u r +1 + C r +1
2
(x
= )f ( x 1 4
= )F ( x
اﻷﺻﻠﻴــﺔ
ur ⋅ u ' :