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Numerade Educator

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Problem 6 Medium Difficulty

Find the average value of the function on the given interval.

$ f(x) = \dfrac{x^2}{(x^3 + 3)^2} $ , $ [-1, 1] $

Answer

$\frac{1}{24}$

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Video Transcript

Okay. Once we've used the average value Formula one of the B minus a the bounds of a to B f of X gx. We've right now our equation here. Now we know we can simplify this, and we know we can do U substitution. So say that are you is X cubed plus three. Then d'you would be three ax squared, right? Therefore giving. Given this, we know that if we plug n r two bounds wanted negative one, we have to. Now remember, we also have to multiply by a 1/2. So now we're gonna be doing 1/2 times 1/3 you to know you too, do you? Which gives us 16 times 1/4 with just 1 24th Remember, the integral of you to the night of two is negative. One over you.