topic 15-indefinite integral
TRANSCRIPT
-
8/8/2019 Topic 15-Indefinite Integral
1/4
o{ J T`f D@A ?2=2tlrka =07 Khd`ikhkt` Kht`nmcM qtprkd }p`qtklh kq tf` lh` hlt mqe`d
@7 jmtfq(~(j(t`fBnjmkc(alj
x = xKi {lp ikhd tfkq pq`ipc# AMCC%90*;61? ?2=1 mhd mqe il JL_@
]p`qtklh =7
M apy` il ~fkaf 6: evdv
d{# fmq m qtmtklhm{ rlkht mtv : 4(
&m+ Qtmt` tf` ymcp` lie(&o+ ^ktf tfkq ymcp` li e# ikhd#
&k+ tf` }pmtklh li tf` tmhn ht mt tf` rlkht +0#1& #&kk+ ikhd tf` }pmtklh li tf` apy`(
]p`qtklh ?7
Nky`h tfmt 1+&1
2
:
dvvi mhd 0+&
1
2
:
dvvn # qtmt` ~fkaf li tf`
ilccl~khn kht`nmcq amhhlt o` ymcpmt`d mhd ymcpmt` tf` ltf`q(
&k+ dvvnvi +Z&?+&U12
%
&kk+ dvvnvi +&+&12
&kkk+ dvvndvvi +&+& 12
2
1
&ky+
dvvi
?1
2 +Z&U &y+ dvvidvvi Z=+&UZ=+&U 1
=
=
2%%
]p`qtklh 17
Tf` apy` il ~fkaf?v
ev
dv
d{: ~f`` e kq m alhqtmht# kq qpaf tfmt
tf` tmhn`ht mt &1# =+ rmqq`q tflpnf tf` lknkh( Ikhd
&k+ tf` ymcp` lie#
&kk+ tf` `}pmtklh li tf` apy`(
]p`qtklh 47
&m+
Dkii``htkmt`
0
+>?& v ~ktf `qr`at tlv(&o+ F`ha` ikhd dvvv 41? +>?& (
]p`qtklh 07
Tf` nmdk`ht li m apy` kq nky`h o{ 1: mvdv
d{# ~f`` m kq m alhqtmht(
Nky`h tfmt tf` nmdk`ht li tf` tmhn`ht tl tf apy` kq 0 mt tf` rlkht
+=#?& # ikhd
&m+ tf` ymcp` lim#&o+ tf` }pmtklh li tf` apy (
mailto:[email protected]:[email protected]:[email protected]:[email protected] -
8/8/2019 Topic 15-Indefinite Integral
2/4
o{ J T`f D@A ?2=2tlrka =07 Khd`ikhkt` Kht`nmcM qtprkd }p`qtklh kq tf` lh` hlt mqe`d
@7 jmtfq(~(j(t`fBnjmkc(alj
x ? xKi {lp ikhd tfkq pq`ipc# AMCC%90*;61? ?2=1 mhd mqe il JL_@
]p`qtklh 97
Nky`h tfmt+=?&
=
=?ch
%:
% vvv
v
dv
d( F`ha` l ltf`~kq`# `ymcpmt`
(+=?&
?191
=
?
dvvv
vv %
%%
]p`qtklh >7
&m+ Ikhd & +=4 %vvdv
d(
&o+ F`ha`# ymcpmt`
dvv
v %
%?2 =4
?=? (
]p`qtklh 67
Tf` nmdk`ht li tf` hljmc tl m apy` mt tf` rlkht &v# {+ lh tf` apy` kq
vev 1
??
~f`` e kq m alhqtmht( Nky`h tfmt tf` apy` fmq m tphkhn
rlkht mt &9# 1+# ikhd
&m+ tf` ymcp` lie#&o+ tf` }pmtklh li tf` apy #&a+ tf` mhn` li ymcp`q liv il ~fkaf { kha`mq`q mqv kha`mq`q(
]p`qtklh ;7
Ikhd =2
?alq0
v
dv
d
mhd f`ha`# `ymcpmt` 42
4
+?alq?qkh&
dvvvv (
]p`qtklh =27
M apy` rmqq`q tflpnf tf` rlkht
2#
?
mhd ktq nmdk`ht mt mh{ rlkht
+#& {v lh tf` apy` kq +qkh=&qkh vv ( Ikhd
&m+ tf` }pmtklh li tf` hljmc tl tf` apy` mt tf` rlkht :v #&o+ tf` }pmtklh li tf` apy (]p`qtklh ==7
@ymcpmt`
2alq+qkh&alq dvvvv (
]p`qtklh =?7
&m+ Dkii``htkmt` v`vv ?0? ch ~ktf `qr`at tlv(&o+ F`ha` ikhd tf` ymcp` li vvv dch?
= # nkykhn {lp mhq~` kh tf`ilj aom %ch ~f`` m# o mhd a m` alhqtmhtq(
mailto:[email protected]:[email protected]:[email protected]:[email protected] -
8/8/2019 Topic 15-Indefinite Integral
3/4
o{ J T`f D@A ?2=2tlrka =07 Khd`ikhkt` Kht`nmcM qtprkd }p`qtklh kq tf` lh` hlt mqe`d
@7 jmtfq(~(j(t`fBnjmkc(alj
x 1 xKi {lp ikhd tfkq pq`ipc# AMCC%90*;61? ?2=1 mhd mqe il JL_@
]p`qtklh =17
M apy` fmq tf` }pmtklh +?alq?&qkh?
vv`{v : # ~f`` 33 v2 (
&m+ Qfl~ tfmt ve`dv
d{ v?qkh
?: # ~f`` e kq m alhqtmht(
&o+ Qtmt` tf` ymcp` lie(&a+ Ikhd tf`v*alldkhmt`q li tf` qtmtklhm{ rlkht li tf` apy`(&d+ F`ha`# ymcpmt` dvv` v ?2 ? ?qkh
(
]p`qtklh =47
Nky`h tfmt mdvvi :1
2
+& mhd :1
2
?+& mvn # ~f`` m kq m `mc hpjo`#
ikhd tf` ymcp` lim ki :%
1
2
1
2
1
1
2
+&+& dv`dvvndvviv (
]p`qtklh =07
Kht`nmt`v
v
``
?
=% ~ktf `qr`at tlv(
]p`qtklh =97
&m+ @vr`qq10?
?1
?
vv
vkh rmtkmc imatklhq(
&o+ F`ha` `ymcpmt` =?
4 ?d
10?
?1v
vv
v(
]p`qtklh =>7
@vr`qq +0&+=&
1>40?
?
%
vv
vv
mq rmtkmc imatklhq mhd f`ha`# ikhd
% dv
vvvv
+0&+=&
1>40?
?
(
]p`qtklh =67
&m+ Nky`h tfmt :?2 4+& dvvi mhd :0
?=?+& dvvi # ymcpmt`
&k+ 02 +& dvvi #&kk+ 0? +Z&?U dvviv (
&o+ Ikhd tf` ymcp` lij il ~fkaf :%?2 ? 2Z+&U dvjvvi (
mailto:[email protected]:[email protected]:[email protected]:[email protected] -
8/8/2019 Topic 15-Indefinite Integral
4/4
o{ J T`f D@A ?2=2tlrka =07 Khd`ikhkt` Kht`nmcM qtprkd }p`qtklh kq tf` lh` hlt mqe`d
@7 jmtfq(~(j(t`fBnjmkc(alj
x 4 xKi {lp ikhd tfkq pq`ipc# AMCC%90*;61? ?2=1 mhd mqe il JL_@
]p`qtklh =;7
&m+ @vr`qq409
=40
? %
%
vv
vkh rmtkmc imatklhq(
&o+ F`ha` `ymcpmt`
dvvv
v %
%4
=
?409
=40(
]p`qtklh ?27
&m+ @vr`qq?+=?&
+=&?
v
vkh rmtkmc imatklh(
&o+ F`ha`# ymcpmt`
dvvv
1
= ?+=?&+=&? (
mailto:[email protected]:[email protected]:[email protected]:[email protected]