fundamental therom of calculus? Help?

Question

IM having trouble with part two of the fundamental theroum of calculus... any help is appreciated...

Example.....

If F(x) is the anti derivative of of ln x and F(1)=2 then F(9)=????

please help... im having trouble understanding how to do this.

Answer 1

Go to this site:

http://archives.math.utk.edu/visual.calculus/4/ftc.9/index.html

Guido

Answer 2

The fundamental theorem of calculus states that
∫(1..9)ln x dx = F(9)-F(1) = F(9)-2.
So F(9) = 2 + ∫(1..9) ln x dx.
Here the 1..9 means to evaluate the integral
from 1 to 9.
The problem actually doesn't require you
to calculate the integral, just to find F(9)
in terms of it.

Answer 3

If f(x) is an antiderivative of ln x...try finding f(x) first..

f(x) =xln(x) -x + c

Subsitute x = 1 , you get c = 2
f(1) = 1*ln(1) - 1 +c = 2(given) ==> c=2

Then use the same thing to find out
f(9) = 9* ln(9) -9 +2 =( 9 * 2.19722458 ) - 9 +2
=12.7750212

Answer 4

I don't know if you're meant to do this, but you can find the integral of lnx using integration by parts

u = lnx v' = dx
u' = dx/x v = x

integral(ln(x)dx) = xln(x) - integral(dx)

= xln(x) - x + c

For x = 1, F(x) = 2

ln1 - 1 + c = 2

c = 3

F(x) = xlnx - x + 3
F(9) = 9ln9 - 6
= 13.78 to 2dp

Note: previous poster made an error and put c = 2 not 3,
1*ln(1) = 0 not 1

Answer 5

Is the answer 0.222? Let me know somehow. You have us here working on this problem!!!

thanks