Math Insight

Quiz on Riemann sums and definite integrals

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Total points: 7
  1. Approximate the definite integral $\displaystyle \int_{-1}^{1} - t^{3} + 4\, dt$ using a left Riemann sum with $5$ intervals. If rounding, be sure to include at least $5$ significant figures.

    $\displaystyle \int_{-1}^{1} - t^{3} + 4\, dt=$

  2. Evaluate the following integral: $\displaystyle \int_{-1}^{2} 9 e^{- 8 t}\, dt =$

  3. The volume of a cell is given by the function $v{\left (t \right )}=4 t^{2} + 400$ $\mu {\rm m}^3$ from $t=1$ to $t=8$ seconds. What is the average volume of the cell during this time frame?

  4. Evaluate the following integral: $\displaystyle\int_{0}^{2} 10 t^{2} + 8 t - 8\, dt=$

  5. Evaluate the following integral: $\displaystyle \int_{2}^{6} - \frac{1}{5 t}\, dt =$

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Math 201, Spring 2015