If $\int_0^1f(x)\,dx=16$ and $\int_0^1g(x)\,dx=3.5$, then determine $\int_0^14\cdot f(x)-8\cdot g(x)\,dx$.

Use Integral Rule 4 which says
$$\int_0^14\cdot f(x)-8\cdot g(x)\,dx=4\cdot \int_0^1f(x)\,dx-8\int_0^1g(x)\,dx.$$
So this is nothing more than Algebra:
$$\begin{eqnarray} \int_0^14\cdot f(x)-8\cdot g(x)\,dx&=&4\cdot \int_0^1f(x)\,dx-8\int_0^1g(x)\,dx\\ &=&4\cdot16-8\cdot 3.5\\ &=&64-28\\ &=&36 \end{eqnarray}$$