For on , the magnitude of the second derivative satisfies for all in the interval.…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

For

f(x)=\ln x

[1,4]

, the magnitude of the second derivative satisfies

|f''(x)|\le 1

for all

x

in the interval. What is the least even integer

n\,(n\ge 2)

such that an approximation of

\displaystyle \int_{1}^{4} \ln x\,dx

using

n

equal-width trapezoids is guaranteed to have an error less than

0.001

? (a)

32

(b)

60

(c)

48

(d)

24