# Math Insight

### Quiz 7

Name:
Group members:
Section:
Total points: 8
1. Evaluate the following integral: $\displaystyle\int 7 e^{8 t}\, dt=$

2. Solve the pure-time differential equation $\frac{d z}{d t} = 4 t^{2} - 8 t + 1$ with initial condition $z{\left (0 \right )} = 2$.
$z{\left (t \right )}=$

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: $\displaystyle \int - \frac{2}{- t + 7}\, dt=$

4. Evaluate the integral: $\displaystyle \int 10 t^{5} + 8 t^{3} - 8 t\, dt =$

5. Use Forward Euler with time steps of size $\frac{1}{2}$ to approximate the solution of the differential equation $\frac{d g}{d t} = - 3 e^{- 3 t}$ at time $t=4$, given that $g{\left (2 \right )}=-1$. If rounding, be sure to include at least $5$ significant figures.