formuals and theorems 3

properties of lnx

1. ln(ab)= lna+lnb

2. ln(a/b)= lna-lnb

3. lna^r =rlna

properties of the definite integral

1. integral from a to b c•f(x)dx=

2. integral from a to a f(x)dx=

3. integral from b to a f(x)dx =

4. integral from a to b f(x)dx =

1. c integral from a to b f(x)dx, c is a nonzero constant

2. 0

3. negative integral from a to b f(x)dx

4. integral from a to c f(x)dx + integral from c to b f(x)dx ,where f is continuous and order doesn’t matter for a, b, and c

fundamental theorem of calculus

1. integral from a to b f(x)dx=F(b)-F(a), where F’(x)=f(x)

2. d/dx integral from a to x f(t)dt =f(x) and d/dx integral from a to g(x) f(t)dt = f(g(x))•g’(x)

that’s it

.