ANSWER

Step-by-step explanation
Given;

The average temperature from month 3 to month 6 ;
This will be the average value of the function over the interval (a,b);
Hence;

Substituting the values, we have;

Take constant out;

Apply sum rule;

Using integral substitution;

At t=3;

At t=6;

Now, we have;
![\begin{gathered} \int _{(\pi )/(2)}^(\pi )\cos \left(u\right)(6)/(\pi )du \\ 13\cdot \int _{(\pi )/(2)}^(\pi )\cos \left(u\right)(6)/(\pi )du \\ 13\cdot (6)/(\pi )\cdot \int _{(\pi )/(2)}^(\pi )\cos \left(u\right)du \\ 13\cdot (6)/(\pi )\left[\sin \left(u\right)\right]^(\pi )_{(\pi )/(2)} \\ (78)/(\pi )\left[\sin \left(u\right)\right]^(\pi )_{(\pi )/(2)} \\ 2\left(-\left(-(78)/(\pi )\right)+72\right) \\ 2\left((78)/(\pi )+72\right) \\ (2\left(78+72\pi \right))/(3\pi ) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/7lsispavk9k7uecxpxymfi791nmoiiqe98.png)