Exarcise 2: (Exercise 2 page 138) (3points)\ Suppose

f>=0,f

is continuous on

a,b

and

\\\\int_a^b f(x)dx=0

\ Prove that

f(x)=0

for all

xin[a,b]

.\ Exercise 3: (Exercise 4 page 138 ) (3points)\ If

f(x)=0

for all irrational

x,f(x)=1

for all rationd

x

\ prove that

f!inR

on

a,b

for any

a.

Exarcise 2: (Exercise 2 page 138) (3points) Suppose f0, f is continuous on [a,b] and abf(x)dx=0 Prove that f(x)=0 for all x[a,b]. Exercise 3: (Exercise 4 page 138 ) (3points) If f(x)=0 for all irrational x,f(x)=1 for all rationd x prove that f/ on [a,b] for ary a