Math Insight

Quiz on Riemann sums and definite integrals

Name:
Group members:
Section:
Total points: 7
  1. The volume of a cell is given by the function $v{\left (t \right )}=4 t^{2} + 400$ $\mu {\rm m}^3$ from $t=3$ to $t=9$ seconds. What is the average volume of the cell during this time frame?

  2. Evaluate the following integral: $\displaystyle\int_{-1}^{1} - 7 t^{2} - 7 t - 3\, dt=$

  3. Approximate the definite integral $\displaystyle \int_{-1}^{0} - 3 t^{2} + 8\, dt$ using a left Riemann sum with $4$ intervals. If rounding, be sure to include at least $5$ significant figures.

    $\displaystyle \int_{-1}^{0} - 3 t^{2} + 8\, dt=$

  4. Evaluate the following integral: $\displaystyle \int_{-1}^{0} e^{- t}\, dt =$

  5. Evaluate the following integral: $\displaystyle \int_{1}^{3} - \frac{3}{5 t}\, dt =$