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02 intégrale sur un segment d une fonction continue par morceaux
- 1. ! "
# ! <
$ % & !
' & ! [ ]# $#"""#( ) *
=<<<= """) "
% $#"""#( )=σ $+#"""+#+(+ )=σ & ! [ ]# #
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% $#"""#( )=σ $+#"""+#+(+ )=σ & ! * *
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1 # * & [ ]# (*
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- 2. $
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] [#− " ! &
=
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[ ]
)
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[ ] [ ] [ ]
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µλµλ
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[ ] [ ] [ ]
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% $(−
ε & ϕ [ ]# * ( + 3 3
* ≤ϕ $
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- 3. 8
% $(+
ε & ψ [ ]# * ( + 3 3
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#
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##
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≤ "
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- 4. <
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$"
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)
)
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1
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% )>ε
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)>α *
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εϕ ≤−
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- 5. ?
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2 #
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% [ ]# " #
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ψϕ ≤≤ εϕψ ≤−
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++ ψϕ ≤≤ εϕψ ≤− # ! # ψϕ ≤≤ εϕψ ≤− #
! εϕ ≤− "
$ * &
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#
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- 6. ' * [ ]# * #
ε # ϕ ψ [ ]# *
ψϕ ≤≤ εϕψ ≤− "
& # *
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5 [ ]# 6# #
2 # ! * 2 5 [ ]#
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• 0 & & "
% * [ ]#) ( + 3 3 $( = ∈ # ) $
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! "
# ε * ) << ε " [ ]#ε #
& # ! # ϕ ψ [ ]#ε #
ε " % ϕ ψ [ ]#) $( −=ϕ $( =ψ [ [ε#)∈ #
* ϕ ψ [ ]#) # * ψϕ ≤≤ # *
[ ] [ ] [ ] [ ]
εεεεϕψϕψϕψ
εε
8$(
##)#)#)
≤−+≤−+−=−
1 7# 2 )$($( =− −+
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% [ ]#)
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( { })B∈ $" # * ε 2
(! * C ( * ε< $#
[ ]#) ) # ! ] ]# $
# # & " ( −=
π
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