Mathematics

Problem

Let

f(x)=\ln(1+x)

[0,2]

. A trapezoidal estimate with four equal subintervals gives

\displaystyle\int_{0}^{2}f(x)\,dx\approx1.6479

. Knowing that

|f''(x)|\le\dfrac{1}{(1+x)^{2}}

for all

x

[0,2]

, determine an upper bound on the possible error in the corresponding average value. Express your bound as a decimal to three significant figures.