Question

I'm having trouble with this problem on my homework.

Answer 1

The average value of f(x) on the interval x=0 to x=12 is 5.

The average value of a function f(x) on the interval [a, b] can be calculated using the formula:

`\[ \text{Average value} = (1)/(b - a) \int_(a)^(b) f(x) \, dx \]`

In this case, the interval is from x = 0 to x = 12, and the given integral is
`\(\int_(0)^(12) f(x) \, dx = 60\)`.

Therefore, the average value is:

`\[ \text{Average value} = (1)/(12 - 0) * 60 \]`

`\[ \text{Average value} = (1)/(12) * 60 \]`

`\[ \text{Average value} = 5 \]`

So, the average value of f(x) on the interval [0, 12] is 5.