Math Insight

Quiz on Riemann sums and definite integrals

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Total points: 7
  1. The volume of a cell is given by the function $v{\left (t \right )}=700 + 100 e^{- 2 t}$ $\mu {\rm m}^3$ from $t=1$ to $t=5$ seconds. What is the average volume of the cell during this time frame? If rounding, be sure to include at least $5$ significant figures.

  2. Approximate the definite integral $\displaystyle \int_{-1}^{1} - 2 t^{3} + 6\, dt$ using a left Riemann sum with $4$ intervals. If rounding, be sure to include at least $5$ significant figures.

    $\displaystyle \int_{-1}^{1} - 2 t^{3} + 6\, dt=$

  3. Evaluate the following integral: $\displaystyle \int_{3}^{6} - \frac{1}{2 t}\, dt =$

  4. Evaluate the following integral: $\displaystyle\int_{0}^{1} 2 t^{2} + 6 t + 9\, dt=$

  5. Evaluate the following integral: $\displaystyle \int_{1}^{2} 8 e^{2 t}\, dt =$