Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.71

12. x 3x 7 dx(^2 + )^7 ( )
    Ans. 3x 7^128
    48

(^) +

13. 2

xdx

(^) 3x 4+
3x 4^2
Ans. 3
(^) +
(^)

14. (i) (2x 3 x 3x 1dx+ ) (^2 + −) ( )
    Ans. x 3x 1^22 3/2
    3

(^) + −
(^)
(ii)
x 2 dx
2x 8x 5

−

(^) − +
Ans. 2x 8 5^12
2
(^) − +
(^)

15. (i)

2

3 4

t dt

(^) t 3+ ( )
Ans. t 3^34 2/3
8
(^) +
(^)
(ii) 3 2
x 2 dx
x 4x 5

−

(^) − + ( )
Ans. x 4x 5^32 2/3
4
(^) − +
(^)

16.

dx

(^) xlogx [Ans. logx] 17.
log x
(^) 3x ( )
2
(^) Ans. log x (^)

18. (I) ( )( )

x 1 x logx dx^2

x

+ +

Ans. (x log)^13

2

(^) +
(^)
(ii) {^2 }
dx
(^) x 12 7logx (log)+ + [Ans. log (log x + 3) – log(log x + 4)
(iii) 2
dx
(^) x(logx) 4xlogx 12x+ −
Ans. log(log 2) log(logx 6)^11
8 8
(^) − − +
(^)
19. (i) (^) 3x 7^2 x 1+− dx
Ans. x log(3x 7)^217
2 9
(^) − +
(^)
(ii) (^2) 3x 2x 3++ dx
Ans. x log(3x 2)2 5
3 9
(^) + +
(^)

20. a bxc dx++ dx 2
    Ans.bx (ad bclog(c dx)
    d a

(^) + − +
(^)

21. x 2
    e 1 1 dx
    x x

(^) −
(^)
ex
(^) Ans.x (^)
22.
e (x 2)x dx 3
− x
x
2
Ans.e
x
(^)

23. (i)

x x

x x

e e dx

e e

−

−

+

(^) − [Ans. log(e
x – e-x)] (ii)^1 x/2dx
(^) 1 e+ [Ans. –2(e
–x/2 + 1)]