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Why is the area under this curve negative?

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1. When I use a graph sketcher to sketch it, there is no part that goes under the x-axis.

I know that it's negative because

and ln(1/2) is negative, so my answer will be negative. But I don't understand why there is a negative number there. Is it just something I have to ignore? or is there a reason for it?

Wolfram alpha calculates it as postive so maybe my working is wrong? If I'm being really stupid, I'm really sorry
2. Surely the numerator tends to -1
3. (Original post by hello calum)

When I use a graph sketcher to sketch it, there is no part that goes under the x-axis.

I know that it's negative because

and ln(1/2) is negative, so my answer will be negative. But I don't understand why there is a negative number there. Is it just something I have to ignore? or is there a reason for it?

Wolfram alpha calculates it as postive so maybe my working is wrong? If I'm being really stupid, I'm really sorry

4. its -1/Log[1/2] = 1.4426
5. Substitute in Remember that there's another minus sign as the 0 is the lower limit (and the infinite limit disappears).
6. omg. I was putting them in the wrong way round :/ Sometimes I just do stuff the wrong way round for some reason
7. (Original post by atsruser)

How does the evaluation at infinity equal 0?
which tends to as x tends to infinity, right?

I get that but surely isn't valid, as what on earth is ?

EDIT: Nevermind, I was being stupid. Of course, is negative so . Derp.

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