Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.77

(^1) u 4 du (^221) u 4 du 2 2
= 5 + = 5 +

( )

1 u u 4 4^22222

5 2 2 log u u 4

(^) + (^)
= + + +
(by formula 1)

( )

1 5x 25x 16 16^22

5 2 2 log 5x 25x 16

(^) +
= + + +
(^)

( )

x 25x 16 8^22

= 2 + + 5 log 5x 25x 16 c.+ + +

SELF EXAMINATION QUESTIONS

Integrate :

1. x^2 ex. [Ans. x^2 ex + 2ex – 2xex, c is added in every case]


2. xe4x [Ans. ( )
   e4x
   16 4x 1− +c^ ]


3. xeax. [Ans. ( )

ax

2

e ax 1

a − +c]

4. x log x [Ans.
   x^2 x^2
   2 logx− 4 +c]


5. x^3 ex. [Ans. x^3 ex – 3x^2 ex + 6xex – 6xx]


6. (log x)^2. [Ans. x (log x)^2 – 2x log x + 2x+c]


7. x (log x)^2. [Ans. ( )
   x^22 x^2 x^2
   2 logx − 2 logx+ 4 +c]


8. (i) logxx 2
   Ans. logx 1 c
   x x

(^) − − +
(^)
(ii) 2
log(1 x)dx
(1 x)

+

+

Ans. logx 1 c

x x

(^) − − +
(^)

9. (x + 1)^2 log x
   1 3 1 x 3 2 1
   Ans. logx(x 1) x 3 + −9 2 3− − −x logx c+^
   10.^12 log(logx). [Ans. log x {log(logx)–1}+c]