5

Point) Find the average value of f(x) = Tx + 6 over [1,5]average value...

Question

Point) Find the average value of f(x) = Tx + 6 over [1,5]average value

point) Find the average value of f(x) = Tx + 6 over [1,5] average value



Answers

Suppose that the average value of a function $f(x)$ over the interval [0,2] is 5 and the average value of $f(x)$ over the interval [2,6] is $11 .$ Find the average value of $f(x)$ over the interval [0,6].

We're being asked to find the average value of root experts six from the interval of three detent. So that's going to be found by taking one over the difference of the limits of integrations 10 minus three. The integral from 3 to 10 of root X plus six d x. So this is one over seven and the anti derivative of root X plus six is I found by using the chain room so to over three times X plus six to the power of three over two. Didn't evaluate this from 10 3 Detective. So one over seven putting some values in there. If I put 10 I'm gonna have to over three times 16 to the power of three over two minus. Uh, putting three in there would give me to over three nine to the power of three over two. That's going to simplify Thio 128 over three, and that one is 54 over three. So we've got a common denominator and if we multiply it by one over seven, this works up to 74 over 21

In this question it is told that we have to find the average value of the function. That is a taxi. That was two extra divide by The square root of access were plus 16. And I did in the interval of 0-3. So I'm going to write the formula forever. Its value that is one divide by b minus integration of the tax function in the limits of it to be okay. So I'm going to put here the value of N B n b r 0 to 3. So I get one divide by three minus zero. Integration limits 0 to 3 and actually divided by the square root of taxes square plus 16. Okay now we can see that were integrated. We have to make a substitution here that I'm going to use a us it was to access for plus 16. Now it's a derivative is the US. it was to to work said Yes. Okay now you can see that we cannot use the old limits because all limits stands for the X. Variable that are zero N. Three and were able to find for the U. Variable here use access square plus 16. So we put here zero, then we get here zero plus 16 30 16 and we put here three. Then we get here threes were plus 16. And that is I can say that nine. So I can see you're Now my formula changes into Integration limits are I can see a 9 to Sorry, three square plus 16 turns out into 25 years. Okay, so the limits of integration are I can say that 16-25 years and after substitution what we got here A year. Numerous active X 30 X is replaced by you can see here from this condition extra dx is replaced by Dubai too. So I have to substitute. Do you buy two and divide advice where to talk to you? Okay no further we can see that I can take this one by two constant outside. So I get here one by three into one by two. And now integration of we have to do one upon square ot Okay it's integration is given by a power roll and after integrating it regard here simply two times of where would you? And in this integration we have to substitute the limits. Okay you can also Say one more thing if I take two constant outside. So get here one x 3 and a square out of you and 16-25. Now, first of all we have to vote here upper limit. When I put 25 I get square root of 25 minus square out of 16. Okay now square out of 25 days five so I get here five and minus square out of 16 is four. So I got here five minus four. That is one. So answer for this question is one by three. Okay, thank you.

So the first judge you find the integration four minus 123 on the function You thanks to six X square. Thanks. I got you fishing Hired. True. Thanks, Moe. Long run my guest Shoe Expo Extra minutes one too True. So we have to a billet three inside We bonded you tears 321 you owe I'm not two to this one. You're gonna like this one. You sang gon junior, huh? Blindness two. Thank you. Include you. Thank you. One moment You Why must you and then my mother 50 from minus two? So you look good, you thio minds Wanna know? What did you do for a day? I must do so You didn't go to ah food Just six minutes. Six average. But you know what? I must extremity Virus three minus minus one About your mind? Yeah, for a few minutes

A problem. Number three. Ah, I go to Japan. You is equal to 1/3 minus one in figure from 1 to 3 or three x d x, which is equipped with half times 3/2. X square from 1 to 3. Place of institution here we can get the partner countries.


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