# Integration by substitution

## Homework Statement

Evaluate the definate integral of the following
$$\int$$ (from 1 to 2) $$\frac{sin t}{t}$$ dt

## 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)

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?

rock.freak667
Homework Helper
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.

\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

Defennder
Homework Helper
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.

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.
$$\int_1^2$$

Click on the latex and you will see the code.