If f(x)>0 for all xElement-ofsymbol [a,b], then

b

Integral sign f>0

a

a) Give an example where f(x)>0 for all xElement-ofsymbol [a,b], and f(x)>0 for some xElement-ofsymbol [a,b], and

b

Integral sign f=0

a

b) Suppose that f(x)>0 for all xElement-of symbol[a,b] and f is continous on at x0 in [a,b] and f(x0)>0. Proove that

b

Integral sign f>0

a