Integration by substitution

  • Thread starter ada0713
  • Start date
  • #1
45
0

Homework Statement


Evaluate the definate integral of the following
[tex]\int[/tex] (from 1 to 2) [tex]\frac{sin t}{t}[/tex] 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)

Please help me with the start!!
 

Answers and Replies

  • #2
45
0
I set:
u=sint dv=1/t dt
du=-cost v=lnltl

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

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

How do I integrate the red part?
should I do the by parts again?
 
  • #3
rock.freak667
Homework Helper
6,223
31
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
1,753
1
For your latex

\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 :-p
 
  • #5
Defennder
Homework Helper
2,591
5
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
1,753
1
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.
[tex]\int_1^2[/tex]

Click on the latex and you will see the code.
 

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