Paper 4: Fundamentals of Business Mathematics & Statistic

3.80 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Calculus

h 0

limh a(b a) (b a)(b a h)

→ 2

=^ − + − − +^

( ) ( ) ( )

b a^2 b a

=a b a− + − 2 = b a a−^ + − 2

( ) ( ) (^22 )

b a b a^1 b a

2 2

= − + + = −

Example 165:By the method of summation, find the value of

1

0

(3x 5)dx+

Here, f(x) = (3x+5); a = 0, b = 1;

f(a + rh) = 3 (a + rh) + 5 = 5 +3rh, nh = b – a = 1 – 0 = 1

(^1) n n
∴ 0 (3x 5)dx limh f(a rh) limh (5 3rh)+ =h 0→ (^) r 1= + =h 0→ (^) r 1= +
=h 0limh 5n 3h(1 2 3 ... n) limh 5n 3h.→ { + + + + + }=h 0→^ + n(n 1) 2 +^
h 0 h 0
lim 5.nh (nh)(nh h) lim 5.1 .1.(1 h)^33
→ 2 → 2

= + =^ + +^

5.1 .1.1 5^3 3 10 3 13.

2 2 2 2

= + = + = + =

SELF EXAMINATION QUESTIONS

1.

b

a

dx [Ans. b – a] 2.

b

a

10dx. [Ans. 10(b–a)

3.

b 3

a

x dx [Ans.^1 (b a )^44

4 − ] 4.

1

0

dx [Ans. 1]

5.

1

0

xdx [Ans.^1

2 ] 6.

(^12)
0
x dx [Ans.^1
3

7.

(^22)
1
5x dx [Ans.^35
3 ] 8.
1
0
(2x 5)dx+ (Ans. 6]