Diff&integral Formula

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( )

G DX GX = (OQD )D X  G[ G[ GHX G[ HXGXG[ GXY G[ YXY±GXG[OQX XYGYG[ GVLQX G[ FRVXGXG[ GFRVX G[ ±VLQXGXG[ GWDQX G[ VHFXGXG[ GFRWX G[ ±FVFXGXG[ GVHFX G[ VHFXWDQXGXG[ GFVFX G[ ±FVFXFRWXGXG[

(

)

(

)



 GX G VLQ −X = G[  − X  G[



G FRV −X =− G[



(

−

 − X

(− π  ≤ VLQ

)

(− π  < WDQ

G WDQ X  GX = G[  + X  G[

(

)

(

)

G FRW −X  GX  =− G[  + X  G[

 G VHF −X GX =  G[  X X −  G[

( ≤ VHF

(

−

( ≤ FRV

GX G[



−

( < FRW

)(

[ VLQ  [  −   [ VLQ  [   ò FRV  [G[ = +    ò[VLQ[G[ VLQ[±[FRV[  ò[FRV[G[ FRV[[VLQ[  òVLQ[FRV[G[ VLQ[  FRV(D − E )[ FRV(D + E )[ −  ò VLQ D[ FRV E[ G[ = − (D − E ) (D + E )  òWDQ[G[ ±OQ⏐FRV[⏐ OQ⏐VHF[⏐  òFRW[G[ ±OQ⏐FVF[⏐ OQ⏐VLQ[⏐  òWDQ[G[ WDQ[±[  òFRW[G[ ±FRW[±[  òHD[G[ D HD[  ò[HD[G[ HD[D D[±   òOQ[G[ [>OQ[ ±@ G[  [ = WDQ −  ò   D D D +[

 ò VLQ  [G[ =

)

X≤π  

−

−

−

)

X≤π 

X<π 

)

)

( < FVF

−

)(

X ≤ π  − π < FVF −X ≤ − π 

)

[! 

(D ≠ ) 

(DF − E





>

)

 D[ + E − E  − DF G[ = OQ  E D[ + E[ + F E  − DF D[ + E + E  − DF ò

)

G FVF −X GX  =−  G[  X X −  G[

)

≠ E 

æ Dö  G[ − ç ÷ [ = WDQ (D >  F > )  ç F÷ D[  + F DF è ø  D[ + E G[ WDQ − = ò   D[ E[ F + + DF − E DF − E  D 

)

X < π  − π ≤ VHF X < − π 



 ò

X<π 

−

(D

(E



F ò



G[ D[  + E[ + F

=−

  D[ + E

(E







− DF > 

− DF = 

)

)