# Integration by substitution

1. Jan 23, 2008

1. The problem statement, all variables and given/known data
Evaluate the definate integral of the following
$$\int$$ (from 1 to 2) $$\frac{sin t}{t}$$ dt

3. The attempt at a solution

I am actually stuch from the very beginning.
I tried to set u=sin(t) but this doesn't help much because (sint)'=cost and
this is going to make the problem more complicated.
I also set u=1/t but the derivative of 1/t has nothing to do with
the function as well.

(Perhaps I shouldn't integrate the function by substitution)

2. Jan 23, 2008

I set:
u=sint dv=1/t dt
du=-cost v=lnltl

$$\int$$ [from 1 to 2] (sint)(1/t) dt

= [(sint)(lnltl)]$$^{1}_{2}$$ -$$\int$$[from 1 to 2] lnltl (-cost)

How do I integrate the red part?
should I do the by parts again?

3. Jan 23, 2008

### rock.freak667

Well...I do not think there is any closed form of that integral.(To my knowledge) You may need something more than integration by parts.

4. Jan 23, 2008

### rocomath

\int_1^2

\frac 1 t or \frac{1}{t} - use the brackets when you have more than one letter per term

Or maybe you were lazy

5. Jan 24, 2008

### Defennder

roco, where did you learn the \int_1^2 notation? I never figured it out, at least not from the latex code reference PDF file.

6. Jan 24, 2008

### rocomath

$$\int_1^2$$

Click on the latex and you will see the code.