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]

Question

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]

amistre64 · Answer

height times length .... equals area

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

*compute

anonymous · Answer

I got the answer to be log[2] ?

amistre64 · Answer

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?

amistre64 · Answer

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

anonymous · Answer

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