Reverse Engineering Riemann Sums

If you want to convert a finished riemann sum into its inputs:

• $a$
• $b$
• $x_k$
• $△x=\frac{b-a}{n}$
• $n$
• $f(x)$
• Riemann behavior

Example

Find $a,b,n,△x,x_k$ and riemann behavior of: ${\sum }_{k=1}^4(1+\frac{k}{2})(\frac{1}{2})$

• $n=4$ by sigma notation
• Assume $△x=\frac{1}{2}$ for assumption
  • This means: $\frac{1}{2}=\frac{b-a}{n}=\frac{b-a}{4}$
• Assume $x_k=a+k△x=1+k(\frac{1}{2})$
  • Thus, $a=1$
  • Thus, $b=3$
• This mirrors the right riemann sum Done.