3. Improper Integrals

what are improper integrals

integral from a to ±infinity or -infinity to infinity

write out 3 formats of improper integrals and their limit form

3 steps to solve improper integral

1. take limit of integral as a or b approached ±infinity

2. replace the infinity in the bound with a or b

3. copy integrand

what to do if lower bound is -infinity and upper bound is infinity

split into (lim of -infinity to 0) and (lim of 0 to infinity)

annuity vs perpetuity

annuity: multiple payments a year for T years

perpetuity: 1 payment a year forever

what do the variables represent

PV = present value

m = # of payments a year

P = value of each payment

r = interest rate (5% → 0.05, not 1.05)

T = # of years where annuity is paid

present value of a perpetuity accounting for inflation