Questions: Find the average value of f(x) = 1 + sqrt(x) over the interval [4,25]. 33/7 393/2 99 131/14

Solution Steps

We are given the function \( f(x) = 1 + \sqrt{x} \) and the interval \([4, 25]\). We need to find the average value of this function over the specified interval.

We compute the definite integral of \( f(x) \) from \( a = 4 \) to \( b = 25 \):

\[ \int_{4}^{25} (1 + \sqrt{x}) \, dx = 99 \]

The average value of the function over the interval is given by the formula:

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

Substituting the values, we have:

\[ \text{Average value} = \frac{1}{25 - 4} \cdot 99 = \frac{99}{21} = \frac{33}{7} \]

Final Answer