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Numerade Educator

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Problem 15 Medium Difficulty

Find the average value of $ f $ on $ [0, 8] $.

Answer

$\frac{9}{8}$

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Video Transcript

okay, We know we're gonna be writing some of the areas from our bounds of 0 to 8 aftereffects DX. In this case, we're gonna be counting up and adding all the different areas. So from 01 we see half a square there for the area is negative. 0.5. Remember, it's below the X axis. Stefan's knighted for 123 There's 2/2 spores. This is one 3 to 4 of theirs area of one from 4 to 6. There's area four from 6 to 7. There's an area of 1.5 because there's one and 1/2 square from 7 to 8. There's one square plus half of the squares. So was half of two squares. That's one plus one, which is to I have this hole up and we get nine now. Use the average value Formula one over B minus a. The integral from zero X after vax d ox. In this context, we can plug in one over eight minus zero because we actually know what our A and B is in this problem. Now. We already figured out what is the integral, which is not so. This is 18 times nine, which gives us nine eights is our solution