What is the average value of sqrt [3](x) on the interval -5leqslant xleqslant 9

Question

Answer 1

To find the average value of the function \( f(x) = \sqrt[3]{x} \) on the interval

, we use the formula for the average value of a continuous function over an interval

:

Here, \( f(x) = \sqrt[3]{x} \),

, and

. We need to compute the integral:

First, we find the antiderivative of

:

Now, we evaluate this antiderivative at the bounds

and

:

Next, we calculate \( (9)^{4/3} \) and \( (-5)^{4/3} \):

Thus,

Now, we compute the average value:

Therefore, the average value of

on the interval

is:

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