Mathematics

Problem

A function

g

is continuous on the closed interval

[2,6]

and satisfies

g(x)>0

for every

x

(2,6)

. Answer the following: a. (i) State, with reason, the sign (positive, negative or zero) of the definite integral

\displaystyle \int_{2}^{6} g(x)\,dx

. b. (ii) Can the value of

\displaystyle \int_{2}^{6} g(x)\,dx

ever be zero under the given conditions? Give a brief justification.