Chapter 11.4, Problem 45E

Solution

To find: The correct option from the given options.

The correct option is (B).

Given information:

Which produce typically produces the most accurate estimate of an area under a curve?

NDER, NINT, LRAM, 10 rectangles, RRAM, 25 rectangles, and LRAM, 60 rectangles.

Calculation:

Note that NDER is used to approximate the derivative of the function at a point. To compute an area under a curve, use NINT calculator, or Reimann sums like LRAM or RRAM. In Reimann sums, if the number of rectangles increases, the better approximation with an area under the curve. Thus, LRAM with 60 rectangles gives a better approximation with $\Delta x=\frac{b-a}{60}$ compare to other LRAM, 10 rectangles, and RRAM, 25 rectangles. However, the algorithm for NINT uses Reimann sum with $\Delta x$ varies, that is the number of rectangles might be high to archive better approximation for a given numerical integral.

Thus, the correct option (B).