TMUA Rosie's Papers Set A Paper 1 · Question 17

A student named James Chen is approximating the value of the below integral using the Trapezium rule with $n$ strips.

\int_0^2 x^3-3x^2\,dx.

The approximation is given by $T$ and the true value is given by $I$ , hence which of the following statements is correct?

T<I

for all integers

n\ge1

T>I

for all integers

n\ge1

CThere exists a finite integer

k

such that

T<I

and

n<k

, and

T>I

when

n\ge k

DThere exists a finite integer

k

such that

T>I

and

n<k

, and

T<I

when

n\ge k

EWhether

T>I

T<I

depends on the specific value of

n

, alternating as

n

increases

T=I

for all integers

n\ge1

examday