Riemann Sum for an Improper Integral

Question

The table shows values for right Riemann sum approximations of the integral $$\displaystyle \int_0^1 \frac{1}{x} dx$$ using $$n$$ subintervals of equal width. Which of the following statements best describes the limit of the Riemann sums as $$n$$ approaches infinity?

| $$n$$ | $$\displaystyle \sum_{k=1}^{n} \left(\frac{1}{x_k}\right)\left(\frac{1}{n}\right)$$ |
|-----|-------------------------------------------------------------|
| 100 | 5.19 |
| 200 | 5.88 |
| 300 | 6.28 |
| 400 | 6.57 |
| 500 | 6.79 |

Accepted Answer

The limit of the Riemann sums does not exist because $$\displaystyle \int_0^1 \frac{1}{x} dx$$ does not exist.

Answer

The limit of the Riemann sums is a finite number less than 10.

Answer

The limit of the Riemann sums is a finite number greater than 10.

Answer

The limit of the Riemann sums does not exist because it is a sum of infinitely many positive numbers.

Riemann Sum for an Improper Integral

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