How do you find the average value of $x^{3}$ $x^3$ as x varies between 2 and 4?

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How do you find the average value of $x^{3}$ $x^3$ as x varies between 2 and 4?

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Answer 1 · 2017-02-07T11:53:49

$30$ $30$

Explanation:

The function is continuous in the interval [2 ,4] and the average value from x = 2 to x = 4 is the integral.

$\frac{1}{4 - 2} \int_{2}^{4} x^{3} d x$ $1/(4-2)int_2^4x^3dx$

$= \frac{1}{2} {[\frac{1}{4} x^{4}]}_{2}^{4}$ $=1/2[1/4x^4]_2^4$

$= \frac{1}{2} [\frac{1}{4} \times 4^{4} - \frac{1}{4} \times 2^{4}]$ $=1/2[1/4xx4^4-1/4xx2^4]$

$= \frac{1}{2} (64 - 4) = 30$ $=1/2(64-4)=30$

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How do you find the average value of $x^{3}$ $x^3$ as x varies between 2 and 4?

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