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E\L-LOVELY-H\math13-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12

bdkbZ lekdyu dh fof/;k¡

13-7 lkjka'k uksV

• fdlh iQyu dk lekdyu Kkr djus dh fuEufyf[kr nks eq[; fof/;k¡ gSaµ
izfrLFkkiu }kjk lekdyu
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# "

[k.M'k% lekdyu
,
#

• bl lafØ;k esa fn;s gq, lekdY;
,
dks ekud lw=kksa "
@ esa ifjofrZr
djosQ lekdy fd;k tkrk gSA
• ;fn lekdY;
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φ 0 1 ′ osQ :i dk gks vFkkZr~ ;g fdlh jkf'k osQ iQyu rFkk
blh jkf'k osQ vody xq.kkad ′ dk xq.kuiQy gks ;k bl :i esa fy[kk tk ldrk gks rks ge
bl jkf'k dks # osQ cjkcj ekudj lekdyu djrs gSaA

13-8 'kCndks'k !

1- izfrLFkkiu "

% foLFkkiuA
2- fof/ +
% rjhdkA

13-9 vH;kl&iz'u " ! #

tan 3x
2
1- ∫ sec 3x dx dk eku fudkysaA (mÙkj% 3 + c )

∫ 3 d (mÙkj% − 3 cosθ + 1 cos 3 + θ
2- sin θθ dk eku ifjdfyr dhft,A 4 12 c )
3
cos x
(mÙkj% − +
3- iQyu

dk osQ lkis{k lekdy Kkr djsaA c )
3
 π  sin 2x
 ∫
4- sin 2x +  dx dk eku Kkr djsa (mÙkj% + c )
 2  2

5- ∫ 4sin − x 1 2 ) x ! dk eku fudysa (mÙkj%

/ %)
(1 −

mÙkj % Lo&ewY;kadu

lekdy & / ' !
& $
' & * ' 7 % 8 &