Question

Find the integral of dt/t from x to 2x.

Answer 1

\[\int_x^{2x}\frac{dt}{t}\]?

Answer 2

Yes.

Answer 3

what is the anti deriviative of \(\frac{1}{t}\) ?

Answer 4

That's the part I got stucked.

Answer 5

ok
it is the log

Answer 6

How do I find that?

Answer 7

you don't "find" it, you know it

\[\frac{d}{dt}[\ln(t)]=\frac{1}{t}\]

Answer 8

So it's ln2x-lnx, right? And then it's ln(2x/x)=ln2, right?

Answer 9

yeah i guess so

Answer 10

Thanks.

Answer 11

interesting that it is a constant, right?

Answer 12

Yes.

Answer 13

\[\int_5^{10}\frac{dt}{t}=\ln(2)\]

Answer 14

How about the integral of cos t dt from 1 to x? Isn't it sin(x)-sin(1)?

Answer 15

@satellite73