The Definite Integral as a Limit of Riemann Sums Worksheet with Answer Key

What's on the worksheet

1. Write each limit as a definite integral.
2. Write each integral as a limit of right sums with n equal pieces.
   \displaystyle\int_{-2}^{3} x\,2^{x}\,dx\displaystyle\int_{1}^{4} \dfrac{\ln x}{x}\,dx
3. For each function, decide whether it is integrable on the given interval, and give the reason the lesson's results supply.
4. Compute _3^6 (2x² - 3x)dx from the definition with right endpoints.
5. At a cider mill, Ryan runs a press.
6. Let $f
7. Chloe, Jack and Mei each read the same limit as a definite integral: