Paper 4: Fundamentals of Business Mathematics & Statistic

3.92 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Calculus

Now area P 1 Q 1 Q 2 P 2 P 1 = area P 1 R 1 R 2 P 2 – area Q 1 R 1 R 2 Q 2

( ) ( )

b b

= (^) af x dx 1 − (^) a f x dx 2
{( ) ( )}
b
= f x f x dx 1 − 2
= (^) ab (y y dx, 1 − 2 )
where y 1 and y 2 are the ordinates of the two curves P 1 P 2 and Q 1 Q 2 corresponding to the same abscissa x.
Some Well-known Curves :
It is expected that students are already acquinted with the following well-known curves :

1. Straight line : ax + by + c = 0


2. Circle : x^2 + y^2 = a^2


3. Parabola : y^2 = 4ax


4. Ellipse :

2 2

2 2

x y 1

a a+ =

5. Hyperbola :

2 2

2 2

x y 1.

a b− =