### Home > CALC > Chapter 3 > Lesson 3.4.4 > Problem3-186

3-186.

Write a Riemann sum to estimate $A(f, 5 < x < 13)$ for $f ( x ) = 4 \sqrt [ 3 ] { x - 5 }$ using $n$ left endpoint (or other) rectangles. Then calculate the area for $n = 8$, $20$, and $50$ rectangles. Which is most accurate and why?

Refer to hints in problem 3-177 for further guidance about computing a left-endpoint Riemann sum.

Without a calculator, it is more time consuming to compute a sum with $50$ terms than with $8$ terms. What is the benefit of using $50$ terms?