Page 234 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math13-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV
iz'ukoyh

y?kq mÙkjh; iz'u

fuEufyf[kr dk eku Kkr dhft,µ
3x
& ∫ ax n − 1 b ! ' ∫ (x + 2 4) 5 !
3
n
x +
% ∫ x 2 3 ! ! ∫ e x !
1 − 2x x

mÙkj
a 1
+
& log|x + n b | c ' − (x + 3 4) − 4 + c
n 4
1
% − log |1 − 2x 3 | c+ ! 2e x + c
6 e

Lo&ewY;kadu

cgqfodYih; iz'u @ @ + )

µ
∫ sin x
5- cos xdx dk eku gSµ
1 1
2
2
& sin x + c ' cos x + c
2 2
1
2
% cosec x + c ! buesa ls dksbZ ughaA
2
3
2
∫ cot θ. cosec θ
6- dθ dk eku gksxkµ
4
4
cot θ cot θ
& + c ' − + c
4 4
4
cosec θ
% + c ! dksbZ ughaA
4
)
c
7- sin (log x + fdldk gy gks ldrk gS\
e
2
2
2
2
& ∫ sin x cos xdx ' ∫ cot x cosec xdx
% ∫ cos (log x ) dx ! buesa ls dksbZ ughaA
e
x
+
8- log|1 + e x | c fdldk gy gS\
& ∫ e x dx ' ∫ 1 + e x dx
1 + e x e x
−
x
% ∫ e dx ! ∫ 1 + e e x x dx