Suppose $\int_{-2}^{3} f(x) d x=45$
Then the average value of $7 f(x)$ from $x=(-2)$ to $x=3$ is given by

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Answer

The average value of $7f(x)$ from $x=-2$ to $x=3$ is $\boxed{63}$

Steps

Step 1 ：Suppose $\int_{-2}^{3} f(x) d x=45$

Step 2 ：The average value of a function $f(x)$ from $a$ to $b$ is given by $\frac{1}{b-a}\int_{a}^{b} f(x) dx$

Step 3 ：Given that $\int_{-2}^{3} f(x) dx = 45$, we can substitute this into the formula to find the average value of $7f(x)$ from $x=-2$ to $x=3$

Step 4 ：The 7 is a constant multiplier, so it can be taken out of the integral, giving us $7 \times \frac{1}{3 - (-2)} \times 45$

Step 5 ：The average value of $7f(x)$ from $x=-2$ to $x=3$ is $\boxed{63}$