Review question

If the trapezium rule overestimates $\int^1_0 f(x)\, dx$, what can we deduce? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5324

Question

If the trapezium rule is used to estimate the integral $\int^1_0 f(x)\, dx,$ by splitting the interval $0 \le x \le 1$ into $10$ intervals then an overestimate of the integral is produced. It follows that
1. the trapezium rule with $10$ intervals underestimates $\int^1_0 2f(x)\; dx$;
2. the trapezium rule with $10$ intervals underestimates $\int^1_0 (f(x)-1)\; dx$;
3. the trapezium rule with $10$ intervals underestimates $\int^2_1 f(x-1)\; dx$;
4. the trapezium rule with $10$ intervals underestimates $\int^1_0 (1-f(x))\; dx$.