Page 206 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math12-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV 12-2 ekud lekdy
% &

ekud iQyuksa osQ vody xq.kkad osQ vk/kj ij ge oqQN eq[; iQyuksa osQ lekdyksa dks Kkr djsaxs] tks fuEu gSa%

lekdyu vodyu

∫ xdx = n x n + 1 + c ,(n ≠ − 1) 1 . d (x n + 1 ) = x n
1- n + 1 n + 1 dx

∫ 1 dx = log| | c d (log| |) = 1
x
+
x
2- x dx x
∫ e = x e + x c d (e x ) = e x
3- dx

∫ adx = x a x + c d   a x   = a x
4- log a dx   log a  
e
e
∫ sinx dx =− cosx + c d (cos ) = x sinx
−
5- dx

∫ cosx dx = sin x + c d (sin ) = cosx
x
6- dx

∫ sec x dx = 2 tanx + c d (tan ) = sec x
2
x
7- dx
∫ cosec x dx =− cotx + c d ( cot ) = x cosec x
2
2
−
8- dx
∫ sec tanxdx = secx + c d (sec ) = sec tan x
x
x
x
9- dx
∫ cosec cotxdx =− cosecx + c d ( cosec ) = x cosec x cotx
−
x
10- dx
∫ 1 dx = sin − 1 x + c d (sin − 1 ) x = 1
11-
1 − x 2 dx 1 − x 2

∫ 1 dx = tan − 1 x + c d (tan − 1 ) x = 1
12- 1 + x 2 dx 1 + x 2

∫ 1 dx = sec − 1 x + c d (sec − 1 ) x = 1
13- -
2
2
xx − 1 dx xx − 1