Page 240 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math14-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV
∫
mnkgj.k 2- x sin xdx dk eku Kkr dhft,A
gy % ;gk¡ lekdY; osQ nks xq.ku[kaM gSa] rFkk

nksuksa dk lekdY; Kkr gS ijUrq buesa ls iQyu

osQ izdkj dk gSA blfy, bldks igyk iQyu ekuuk pkfg,A

∫ x sin xdx - x  sin xdx  ∫ −   ∫ d x  ∫ sin xdx dx
vr%  dx       

- x (cos ) − x ∫ 1. ( cos ) dx
−
−
x
-2 x cos x + ∫ cos x dx
-2
/

/ % mÙkj
∫
mnkgj.k 3- x 2 log xdx dk eku Kkr dhft,A

2
gy % ∫ x 2 log xdx
∫ (log x) x dx
x 3 1 x 3
- log x . − ∫ . dx
3 x 3
1 1
2
- x 3 log x − ∫ x dx
3 3
1 1 1 3 

- x 3 log x −  x  + c
3 3 3 

1 1
- x 3 log x − x + 3 . c mÙkj
3 9
∫
mnkgj.k 4- x n log x dk lekdyu dhft,A
∫ x n log xdx
∫ log x xdx
n
gy %
0@ , ftldk lekdyu Kkr ugha gS vr% bldks izFke iQyu eku yks1
x n + 1 1 x n + 1
- log x . − ∫ . dx [k.M'k% lekdyu djus ij)
n + 1 x n + 1

x n + 1 1 x n + 1 1 x n + 1
- log x − ∫ x dx = n log x −
n + 1 n + 1 n + 1 n + 1 n + 1
x n + 1 x n + 1 x n + 1  1 
- log x − =  log x −  + . c mÙkj
n + 1 (n + 1) 2 n + 1  n + 1 

∫
mnkgj.k 5- x 2 cos xdx dk eku Kkr dhft,A

gy % eku yks izFke iQyu gSA
x
∴ ∫ x 2 .cos xdx - x 2 .sin x − ∫ 2 .sin x dx .