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## liliy 2 years ago The Mean Value Theorem of integrals says that if f is continuous on a closed bounded interval [a, b], there exists a number c, between a and b, such that Integral of f[x] dx =f (c) (b - a) Find the value c that satifies the mean value theorem for f(x) = ln(x) on the interval [1,2]

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1. amistre64

height times length .... equals area

2. amistre64

integrate ln(x) from 1 to 2, and divide it by the length of the interval .... stuff like that

3. satellite73

do you know how to compote $\int_1^2\ln(x)dx$?

4. satellite73

*compute

5. liliy

I got the answer to be log[2] ?

6. amistre64

integrate ln(x), xlnx - x (2 ln2 - 2) - (1ln1 - 1) 2 ln2 - 1 ln4 - 1, and since b-a = 2-1 = 1, we get ln(c) = ln4 - 1 c = e^(ln4 - 1) c = 4 - e^(-1) right?

7. amistre64

err, 4e^(-1) might be better

8. liliy

I dont undestnad what i am integrating... you are you also doing xlnx-x?

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