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CHAPTER4: IMPROPER INTTEGRALS NUR IZATI BINTI SUKARA :<3: - Coggle…
CHAPTER4: IMPROPER INTTEGRALS
NUR IZATI BINTI SUKARA :<3:
L'HOPITAL RULE
is used when the function gives
0/0 or ∞/∞
1)
differentiate
numerator and denominator
2) take the
limit
3) if after differentiate the function
still
gives
0/0 or ∞/∞
then,
differentiate again
if
then,
IMPROPER INTEGRAL TYPE I
is used when
one or both limits
are
infinite
if f(x) is continous in interval
[a,∞)
converge
if limit exists OR
diverge
if limit does not exists
if f(x) is continous
(-∞,b]
converge
if limit exists OR
diverge
if limit does not exists
if f(x) is continous in the interval
(-∞,∞)
converge
if both terms converge OR
diverge
if either terms is diverge
IMPROPER INTEGRAL TYPE II
is used when function
interval has values but discontinous
if f(x) is continous in
interval [a,b)
and
discontinous at b
limit exists(
converge
) OR limit does not exist(
diverge
)
if f(x) is continous in
interval (a,b]
and
discontinous at a
if limits exists(
converge
) OR if limit does not exist(
diverge
)
if f(x) has
discontinuity at c
, where
a<c<b
converge
if both terms converge OR
diverge
if either term is diverge