# Math Insight

### Quiz 8

Name:
Group members:
Section:
Total points: 8
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 digits. (To be safe, include even more digits.)

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

$=$

2. 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?

$\mu {\rm m}^3$
For full credit, do not round your answer to a decimal. (Maximum of 80% credit will be awarded for rounded answers that include at least 5 correct significant digits.)

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

If rounding, include at least 5 significant digits in your response.

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

For full credit, do not round your answer to a decimal. (Maximum of 80% credit will be awarded for rounded answers that include at least 5 correct significant digits.)

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

For full credit, do not round your answer to a decimal. (Maximum of 80% credit will be awarded for rounded answers that include at least 5 correct significant digits.)