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I have a problem that I am getting stuck simplifying further.

The problem asks me to find the integral if it exists using Part 2 of the FTC.

I know that the second part of the FTC says:[itex]\int_{a}^{b} f(x)dx = F(b) - F(a)[/itex] Where F is the anti-derivative of f.

Here is the problem:

[itex]\int_{9}^{4} [/itex] x ^-1 dx

While [itex]f(x) = [/itex] x^ -1 is not continuous throughout it is continuous on the interval [4,9]. So therefore it does exist.

So here is my solution:

[itex]f(x) =[/itex] x^ -1

[itex]F(x) = ln|x| + C[/itex]

[itex]F(4) = ln4 + C[/itex]

[itex]F(9) = ln9 + C[/itex]

Here is where I am having trouble simplifying. I would then use [itex]F(b) - F(a)[/itex]

so when I do that I have [itex]ln4 + C - ln9 + C[/itex]

Could I just write that as [itex]ln4 - ln9 + C[/itex] ? Do I still need to simplify further?

Thanks in advance.

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# Homework Help: Part 2 of the Fundamental Theorem of Calculus

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