For , let where is differentiable on . Suppose for all in the interval. What is the…

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

Problem

For

1\le x\le 2

, let

g(x)=\sqrt{1+[f'(x)]^{2}}

where

f

is differentiable on

[1,2]

. Suppose

|g''(x)|\le 1.2

for all

x

in the interval. What is the least even number of equal subintervals needed so that the Trapezoidal Rule approximates

\displaystyle \int_{1}^{2} g(x)\,dx

with an error of at most

0.0005

? (a)

10

(b)

20

(c)

16

(d)

14