Question

can some one please please please help me solve this problem
the file is attached in the answer box

Answer 1

given g(x) is area under the curve f(t) between t=1 and t=x
we know area under a curve is the integral of the curves betwwwn the limits
so
\[G(x)=\int\limits_{1}^{x} 1/t dt\]

Answer 2

now if we integrate to find G(x)
G(x)= [ln t] with lower limit 1 and upper limit x
G(x)=ln x
now G(1)= ln 1 =0
G(1)=0

Answer 3

G(x+h)-G(x) is the area marked in the graph