I am studying for an upcoming Calculus exam, and was hoping someone here could explain how to do the following.
\begin{align} \int_1^9 f(x)\,\mathrm dx&=-1\\ \int_7^9 f(x)\,\mathrm dx&=5\\ \int_7^9 h(x)\,\mathrm dx&=4\\ \end{align}
Find the following:
\begin{align} \int_9^7 [2h(x)-3f(x)]\,\mathrm dx\\ \end{align}
How do I solve this? I believe I can flip the lower/upper limit and use the product rule to get the following, but then what?
\begin{align} \int_7^9 (-2h(x)) \mathrm dx\\ + \int_7^9 (3f(x)),\mathrm dx\\ \end{align}
Hint: integration is a linear operation, you can get (-2) out from integral.