Review question

# Can we use the trapezium rule to estimate this integral? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6592

## Question

When the trapezium rule is used to estimate the integral

$\displaystyle\int_0^1 \! 2^x \, \mathrm{d}x$

by dividing the interval $0 \le x \le 1$ into $N$ subintervals the answer achieved is

1. $\dfrac{1}{2N} \left(1+\dfrac{1}{2^{1/N}+1} \right)$,

2. $\dfrac{1}{2N} \left(1+\dfrac{2}{2^{1/N}-1} \right)$,

3. $\dfrac{1}{N} \left(1-\dfrac{1}{2^{1/N}-1} \right)$,

4. $\dfrac{1}{2N} \left(\dfrac{5}{2^{1/N}+1} -1\right)$.