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Explain how, in general, Riemann sum approximations to the area of a region under a curve change as the number of subintervals increases.

Choose the correct answer below.

A. In general, as the number of subintervals increases, the Riemann sum approximations to the area of a region under a curve become a more accurate estimate of the actual area of the region under the curve.
B. In general, as the number of subintervals increases, the Riemann sum approximations to the area of a region under a curve become a less accurate estimate of the actual area of the region under the curve.
C. No change occurs.

Sagot :

GinnyAnswer
In general, as the number of subintervals increases, the Riemann sum approximations to the area of a region under a curve become a more accurate estimate of the actual area of a region under a curve. This is because the smaller the subintervals (i.e., the more subintervals there are), the closer the sum of the areas of the rectangles used in the Riemann sum approximations will be to the true area under the curve. Reducing the width of each subinterval allows the rectangles to better match the shape of the curve, thereby reducing the overall error in the approximation. Therefore, as the number of subintervals increases, the Riemann sum becomes more precise in estimating the area.

The correct answer is:
OA. In general, as the number of subintervals increases, the Riemann sum approximations to the area of a region under a curve become a more accurate estimate of the actual area of a region under a curve.
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