Average Value of a Function Calculator

The calculator will find the average value of the function on the given interval, with steps shown.

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Solution

Your input: find the average value of $$$x^{4}$$$ on the interval $$$\left[0,7\right]$$$.

The average value of the function $$$f\left(x\right)$$$ on the interval $$$[a,b]$$$ is $$$\bar{f}= \frac{1}{b-a} \int_a^b f \left( x \right) d x$$$.

So, calculate the integral $$$L = \frac{1}{\left( 7 \right)-\left( 0 \right)}\int_{0}^{7} x^{4} d x = \int_{0}^{7} \frac{x^{4}}{7} d x$$$

The calculations and the answer for the integral can be seen here.