Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.61

(ii) ( )
x 22
dx
x

+

2 2

1/2 1/2 1/2 1/2

x 4x 4dx x dx 4 dx 4x dx

x x x x

= + + = + +

(^2) x 4. x 8x 5 /2 (^2) 3/2 1/2 (^2) x5/2 (^8) x 8x c3/2 1/2
= 5 + 3 + = 5 + 3 + +
(iii)
2x 14x 24^2
−x 3− + dx=

( )( )

( ) ( )

x 3 2x 8 x^2

−x 3− − dx 2x 8 dx 2 xdx 8 dx 2. 8x= − = − = 2 −

= x^2 – 8x + c

Example 121:Evaluate ( )

3

2

4x 3

x

−

( )^3

2

4x 3

x

−

3 2

2 2

6 4x 144x 108x 27dx 64x 144 108 27 dx1 1

x x x

= − + − =^ − + −^

(^)
x^2121
=64 144x 108logx 27. 32x 144x 108logx 27 c 2 − + − x= − + + x+
Example 122:Finid e dx4x
4x e4x
e dx= 4 +c. (by formula 5)
Example 123:Evaluate e dx2logx
e dx. e dx x dx2logx logx^22 x^3 c.
= = = 3 +
Example 124: Evaluate
5x 3x
4x
e e dx
e

+

Expression ( )

5x 3x x x

4x 4x

e e dx e e dx

e e

=^ +^ = + −

x x x ex x x

e dx e dx e 1 e e c.

− − −

+ = + − = − +

Example 125: Find the value of

3x 5x

x x

e e dx

e e−

+

(^) +
Expression ( )
( )

( )

( )

4x x x 4x x x 4x 4x

x x x x

e e e e e e e

dx dx e dx 4 c.

e e e e

− −

− −

+ +

= = = = +

(^) + (^) +