Page 44 - Math SL HB Sem 2

Example 14: The growth rate of a city's population has been modeled by the equation
!N = +oo tr05, t> 0 where t is time in years after 1995 and N is the
dt
population size. In the year 2000 the population numbered 32,000. What
will be the population in 2010? Ans: 48606 {698 }

DEFINITE INTEGRALS

Fundamental Theorem of Calculus:
If f(x) is continuous at every point of a , b and ifF(x) is any anti derivative of
I
]
fonIa,b]t]en
fn *= tr(x)I I:FG)-F(a)

Properties of definite integrals:

1 f orr,.lax:t f rlxyax
,.f [ (x) t g(x) d*: f (x) dx t f s(') a*
]
3f f(x)dx= f r1*1 ar* f r1*1 ar;a< c <b

4f (x) dx 0

sf f(x) dx f f(x) dx ; a>b