Mathematics

Problem

A student used left- and right-hand Riemann sums with equal subintervals to approximate

\displaystyle\int_{1}^{2} \ln x\,dx

. The results are given below. n = 4:

L_{4}=0.330

R_{4}=0.411

n = 6:

L_{6}=0.358

R_{6}=0.400

n = 8:

L_{8}=0.369

R_{8}=0.394

n = 10:

L_{10}=0.375

R_{10}=0.391

What is the smallest value of

n

among those shown for which the width of the guaranteed bound on the integral (the difference

R_{n}-L_{n}

) is less than

0.02

? a)

n=8

n=10

n=4

n=6