Page 249 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math15-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 Vth 10-9-12

fJekJh^15 L fBPfus nB[ebB

T[dkjoD 4L f;ZX eo'^ B'N

2
3À/8 tan x dx = À .
tan + cot x 8

∫ À/8 2 2
HHH(1)

HHH(2)

iK T[Zso

gqPBktbh 15H3

ft;Ekog{oD T[Zso tkb/ gqPB

1H f;ZX eo' fe 0 ∫ π /2 log (tan ) dx =
0
x
x dx
2H f;ZX eo' fe 1 ∫ 4 5 x x = 3 .
−+
2
3H f;ZX eo' fe 0 ∫ π /2 1+ dx = π .
4
tan x
sin x
4H f;ZX eo' fe 0 ∫ π /2 sin + cos x dx = π .
4
x

15H5 nBzs ;hwk tkb/ nB[ebB (Integral of Infinity Limit)

i/eo fe;h fBPfus nB[ebB dh T[Zu ;hwk ∞ j't/ sK
a ∫ ∞ f () dx dk noE j? fe lim a ∫ b f ( ) dx
,
x
x
b→∞
gqshpzX fJj j? fe ;hwk e'Jh gfofws (finite) okPh j't/.
i/eo fe;h fBPfus nB[ebB dh fBwB ;hwk –∞ j't/ sK
−∞ ∫ b f () dx dk noE j? fe lim a ∫ b f ( ) dx
x
x
,
a→−∞
gqshpzX fJJ j? fe ;hwk e'Jh gfofws ;zfynk j't/.

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