For a twice-differentiable function on it is known that for all in the interval

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

Problem

For a twice-differentiable function

h

[1,5]

it is known that

|h''(x)| \le 12

for all

x

in the interval. The trapezoidal rule with

n

equal subintervals is used to approximate

\displaystyle \int_{1}^{5} h(x)\,dx

. What is the least integer

n

that guarantees the absolute error of the approximation is at most

0.01

? (a)

n=40

(b)

n=80

(c)

n=57

(d)

n=160