Numerical integration with the trapezium rule Quiz

1. How many ordinates are used for $6$ strips?

• A. $5$
• B. $6$
• C. $7$
• D. $8$

2. Use the trapezium rule with $2$ strips to estimate $\int_0^4\sqrt{x}\,\mathrm{d}x$.

• A. $4.83$
• B. $5.33$
• C. $9.66$
• D. $2.41$

3. For $\int_0^1\mathrm{e}^x\,\mathrm{d}x$ the trapezium rule gives which of these?

• A. An under-estimate, because the curve is concave up.
• B. The exact value.
• C. An under-estimate, because the function is increasing.
• D. An over-estimate, because the curve is convex so the chords lie above it.

4. For $\int_1^3\ln x\,\mathrm{d}x$ the trapezium rule gives which of these?

• A. An over-estimate.
• B. An under-estimate, because the curve is concave so the chords lie below it.
• C. The exact value.
• D. It cannot be determined.

5. An increasing function has ordinates $1,3,6,10$ at strips of width $2$. Which are lower and upper limits for the area?

• A. $29$ and $38$
• B. $20$ and $29$
• C. $20$ and $38$
• D. $19$ and $38$