Paper 4: Fundamentals of Business Mathematics & Statistic

3.74 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Calculus

1 1 1. (^2) du 1 du 1 2du
2 5 u 2 2u 1 10 u 2 10 2u 1

=^ −^ = −

(^) − + − (^) +
(^1) log(u 2) log(2u 1) log(x 2) log(2x 1) c (^11212)
= 10 − − 5 + = 10 − − 5 + +
Example 156:
3
8
x dx
(^) x 1±

( )

3

42

I x dx

x 1

=

± Let x^4 = u or, 4x^3 dx = du.

( )

2 (^2 )

1 du 1log u u 1

= (^4) u 1± = 4 + ± (by C)

(^48 )

(^1) log x x 1.
= 4 + ±
SELF EXAMINATION QUESTIONS
Evaluate :

1. 2
   6
   x dx
   (^) x 1−
   3
   3
   Ans. log1 x 1
   6 x 1
   (^) −
   (^) + 2. 6
   1 dx.
   (^) (logx) 9− x
   Ans. log1 logx 1
   6 logx 1

−

(^) + (^)
3. (^) 2x 3x 1 2 dx+ −
Ans. log1 4x 3 17
17 4x 3 17
(^) + −
(^) + +
(^)

4. 4 4

xdx

(^) a x+ ( )
Ans. log x a x^1244
2
(^) + +
(^)

5. 2

dx

(^) 16x 9− ( )
Ans. log 4x 16x 9^12
4
(^) + −
(^)

6. (i) 2
   dx

(^) x 2x 1+ −
Ans. log1 x 1 2
2 2 x 1 2
(^) + −
(^) + +
(^)
(ii) (^) 2x 4x 7 (^2) −dx −
Ans. log^1 2(x 1) 3
6 2 2(x 1) 3
(^) − −
(^) − +
(^)
(iii) (^) x 3x 1 (^2) −dx +
Ans. log1 2x 3 5
5 2x 3 5
(^) − −
(^) − +
(^)