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

3-186.

Write a Riemann sum to estimate the area under the curve for $5 ≤ x ≤ 13$ using $n$ left endpoint rectangles given$f ( x ) = 4 \sqrt [ 3 ] { x - 5 }$. Then calculate the areas for $n = 8, 20,$ and $50$ rectangles. Which approximation 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?