29390045 rumus dasar integral fungsi eksponen
TRANSCRIPT
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7/24/2019 29390045 Rumus Dasar Integral Fungsi Eksponen
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Rumus dasar integral fungsi eksponen
1. >+= 1a,0a,calna
au
u 3
2. += cee uu
Contoh :Selesaikanlah integral fungsi eksponen berikut ini :
1.
dxe x
cecedxedxe
:maka
dxdu
xumis
xuux +=+==
=
=
2. + dxe)1e x3x
( ) c)1ecudxudxe1e
:maka
dxedu
)1eumis
!x
!1!
!13x
3x
x
x
++=+==+
=
+=
3.
dxex
3x2
ceceduedxex
:maka
dxx3du
xumis
3x31u
31u
31
3x2
2
3
+=+==
=
=
!.
dxex2x3
ceceduedxex
:makadxx"du
x3umis
2x3"1u
"1u
"1
2x3
2
+=+==
=
=
#. ++ dxe)3x x"
2x
ceceduedxe)3x
:maka
dx)3x2dx)"x2du
x"xumis
x"2x21u
21u
21x"2x
2
+=+==+
+=+=
+=
++
1
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Contoh intergal parsialSelesaikanlah integral parsial berikut ini :
1. dxex x
ceexdxeexdxex
:maka
e$
dxed$
dxdu
xumis
xxxxx
x
x
+==
=
=
=
=
2. dxex x23
x2
21
x2
2
x22
23x23
212x2
21x2
213x23
x2
21
x2
2
3
e$
dxed$
dxx2du
xumis
dxexexdxx3eexdxex
:maka
e$
dxed$
dxx3du
xumis
=
=
=
=
==
=
=
=
=
2
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[ ]
[ ]
[ ][ ]
ceexexex
dxeexexex
dxexeexex
dxeexexex
dxxeexexdxex
:maka
e$
dxed$
dxdu
xumis
dxxeexex
dxexexex
dxx2eexexdxexexdxex
:maka
x2
%
3x2
!
3x22
!
3x23
2
1
x2
!
3x2
!
3x22
!
3x23
2
1
x2
2
1x2
2
1
2
3x22
!
3x23
2
1
x2
2
1x2
2
1
2
3x22
!
3x23
2
1
x2
2
3x22
!
3x23
2
1x23
x2
2
1
x2
x2
2
3x22
!
3x23
2
1
x2x22
2
1
2
3x23
2
1
x2
2
1x2
2
12
2
3x23
2
1x22
2
3x23
2
1x23
++=
+=
+=
+=
+=
=
=
=
=
+=
=
==
3. dxxsinex
xsin$
dxxcosd$
dxedu
eumis
dxexcosxcosedxexcosxcosedxxsine
:maka
xcos$
dxxsind$
dxedu
eumis
x
x
xxxxx
x
x
=
=
=
=
+==
=
=
=
=
3
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[ ]
( ) ( )xsinxcosexsinexcosedxxsinesehingga
xsinexcosedxxsine2
aselan&utn'
xsinexcosedxxsinedxxsine
aselan&utn'
dxxsinexsinexcose
dxexsinxsinexcose
dxexsinxsinexcosedxxsine
:maka
x21xx
21x
xxx
xxxx
xxx
xxx
xxxx
+=+=
+=
+==+
+=
+=
+=
TUGAS 6Selesaikanlah integral berikut ini dengan metode parsial :
1. dttsinet
2. dxex x2
3. dxxcosx2
!. dxex2
x#
#. drrcosr2
!