Let $$\begin{aligned} \int_{0}^2 f(x) \, dx & = -9,& \quad \int_{0}^3 f(x) \, dx & = 2, \\ \int_{0}^2 g(x) \, dx &= -10,& \quad \int_{2}^3 g(x) \, dx &= 9. \end{aligned}$$ Use these values to evaluate the given definite integrals.

1. $\displaystyle{ \int_{0}^2 \left(f(x) + g(x)\right) \, dx = }$
2. $\displaystyle{ \int_{0}^3 \left(f(x) - g(x)\right) \, dx = }$
3. $\displaystyle{ \int_{2}^3 \left(3f(x) + 2g(x)\right) \, dx = }$
4. Find the value $a$ such that $$\int_{0}^3 \left(a f(x) + g(x)\right) \, dx = 0.$$ $a =$