Quiz on Forward Euler and indefinite integrals

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Total points: 7

Evaluate the following integral: $\displaystyle \int - \frac{2}{- t + 7}\, dt=$
Solve the pure-time differential equation $\frac{d z}{d t} = 4 t^{2} - 8 t + 1$ with initial condition $z{\left (0 \right )} = 2$.
$z{\left (t \right )}=$
Evaluate the following integral: $\displaystyle\int 7 e^{8 t}\, dt=$
Evaluate the integral: $\displaystyle \int 10 t^{5} + 8 t^{3} - 8 t\, dt =$
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.