Mid-ordinate and Simpson's rules Quiz

1. Using four strips on $[0,2]$, what is $h$?

• A. $2$
• B. $4$
• C. $0.25$
• D. $0.5$

2. Simpson's rule is applied with $n=4$. Which is the correct pattern of coefficients?

• A. $1,2,4,2,1$
• B. $1,4,2,4,1$
• C. $1,4,4,4,1$
• D. $1,2,2,2,1$

3. Mid-ordinate rule, $\int_0^4f(x)\,dx$ with two strips: where is $f$ evaluated?

• A. $x=1$ and $x=3$
• B. $x=0$ and $x=2$
• C. $x=2$ and $x=4$
• D. $x=0,2,4$

4. Simpson's rule with $h=0.5$ uses ordinates $y_0=1$, $y_1=2$, $y_2=5$. Find the estimate.

• A. $3.5$
• B. $\frac{14}{3}$
• C. $\frac{7}{3}$
• D. $7$

5. $f(x)$ has $f''(x)<0$ on $[a,b]$. The mid-ordinate rule gives:

• A. an exact value
• B. an overestimate
• C. an underestimate
• D. no estimate