Question

Find the value(s) of c guarenteed by the Mean Value Theorem for Integrals for the function over the closed interval.
f(x) = x-2x^1/2 [0,2]

Answer 1

@ChmE @agent0smith @Carl_Pham @SamuelAlden917
anyone? my teacher didn't explain this, and i'm so confused...

Answer 2

\[\int\limits_{0}^{2}x-2x^{1/2}dx\]

Answer 3

can you integrate this by yourself

Answer 4

yeah, thanks

Answer 5

\[{x^2 \over 2}-2x^{3/2}\frac{ 2 }{ 3 }={x^2 \over 2}-{4x^{3/2} \over 3}|_{0}^{2}\]

Answer 6

did you get the same thing?

Answer 7

Now we have to plug in 2 for x and subtract plugging in 0 for x

Answer 8

where'd u get the 2/3 from?

Answer 9

http://www.sosmath.com/calculus/integ/integ04/integ04.html
2/3 came from the 3/2 in the denominator. cuz you add one to the power all over the power. So i flipped it to change it to multiplication

Answer 10

So I don't remember how to find c. I don't remember doing this type of problem. The integration is right. So now we have to work together with the link I posted to find c.

Answer 11

yeah i got the F(x) same thing..

Answer 12

Ok i got it

Answer 13

http://www.dummies.com/how-to/content/using-the-mean-value-theorem-for-integrals.html
Scroll down to the bottom

Answer 14

ok i think i got it.

Answer 15

\[f(c)=\frac{ 1 }{ 2-0 }[({(2)^2 \over 2}-{4(2)^{3/2} \over 3})-({(0)^2 \over 2}-{4(0)^{3/2} \over 3})]\]

Answer 16

Post your answer I'll check it with mine

Answer 17

yeah i got the same thing on paper.

Answer 18

my final answer is\[1-\frac{ 4\sqrt2 }{ 3 }\]

Answer 19

i got
\[2-\frac{ 8\sqrt{2} }{ 3 }\]

Answer 20

don't forget about distributing the 1/2

Answer 21

whoops i forgot to multiply by 1/2

Answer 22

NIce job. I learned something tonight too

Answer 23

wait...
there are two answers.....
0.4380, 1.7908

Answer 24

Is that what the book says?

Answer 25

yeah

Answer 26

I don't see how

Answer 27

either of those answers don't match ours

Answer 28

this is what the answer thingy says

Answer 29

i think i can try to figure it out.

Answer 30

I see it

Answer 31

sorry i'm a little lost...

Answer 32

We got our f(c) right. \[f(x) = x-2x^{1/2}\]\[f(c)=1-\frac{ 4\sqrt2 }{ 3 }\]\[c-2c^{1/2}=1-\frac{ 4\sqrt2 }{ 3 }\]Solve for c

Answer 33

They entered c in for x in the original formula and set it equal to f(c)

Answer 34

ohh i see it.

Answer 35

The next step looks like they completed the square

Answer 36

Then it gets really messy

Answer 37

At least you know the basics of how to find c now

Answer 38

ok thanks.