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 :
- Straight line : ax + by + c = 0
- Circle : x^2 + y^2 = a^2
- Parabola : y^2 = 4ax
- Ellipse :
2 2
2 2
x y 1
a a+ =
- Hyperbola :
2 2
2 2
x y 1.
a b− =