Simple Integration by Substitution

In summary, a student is seeking help with a simple integration by substitution problem involving the integrand f(x) = x* sqr(x-1) on the interval [1,2]. A user suggests drawing it out and sending it as a gif file via email. Another user advises the student to attempt the problem themselves and offers a helpful substitution. The student eventually receives a solution and the conversation shifts to discussing different approaches. A user expresses concern that the solution was given too easily and suggests leaving some mystery and room for discovery for the student. Another user's solution is removed from the thread.
  • #1
adiles
1
0
Please help. I'm having trouble with a simple integration by substitution problem


The integrand is f(x) = x* sqr(x-1)
The interval [1,2]

Please draw it out in a gif file and send it to me via email.

-much appreciated.
 
Physics news on Phys.org
  • #2
If I tell you how to do the substitution will you try to work it out from there? Or do you want someone to just do your homework for you?
 
  • #3
adiles,

The policy here is that we'll help you if you show what you've tried and where you appear to be stuck.

It seems to me that you may have a problem with algebra (in this case, at least), as the most obvious substitution should get you an easily integrable form.
 
  • #4
Start with [tex]u=\sqrt{x-1}[/tex]
 
  • #5
I wouldn't recommend that.
(but I am interested to see how you worked it out with that sub!)
 
  • #6
Math Is Hard said:
I wouldn't recommend that.
(but I am interested to see how you worked it out with that sub!)

and why not?
::
u=sqrt(x-1)
x=u^2+1
dx=2udu

The integrand becomes (u^2+1)u*2udu
A simple polynomial which has to be integrated from 0 to 1 if i am not mistaken with calculations that are going in my head.
::

-- AI
 
Last edited:
  • #7
Tenali, I wish you hadn't done that in the thread. This leaves adiles with no work to do.
 
  • #8
I would use a slightly different (and simpler in my mind) substitution method, but I'll withhold, just to leave a little mystery and hopefully some "pleasure of discovery" for adiles. :smile:
 
  • #9
since some one already solved it for him, the simplest sub i saw was...

f(x) = x* sqr(x-1)

let
u = x-1
 
Last edited by a moderator:
  • #10
That's why you make the one example something different (but similar enough to demonstrate the point... maybe [itex]\int \sqrt{x-1} \, dx[/itex]) The problem is that all the example in the world usually don't help unless the student actually does a few himself.
 
  • #11
why the hell was my solution erased from this thread?
 
  • #12
Cronxeh I am guessing

Gokul43201 said:
I wish you hadn't done that in the thread. This leaves adiles with no work to do.
 

1. What is simple integration by substitution?

Simple integration by substitution is a method used in calculus to solve integrals that involve a variable raised to a power. It involves replacing the variable with a new one, called the substitution variable, in order to simplify the integral and make it easier to solve.

2. When should I use simple integration by substitution?

Simple integration by substitution is most useful when the integral involves a function that is not easily integrable. It is also helpful when there is a variable raised to a power that can be simplified by using a substitution.

3. How do I perform simple integration by substitution?

To perform simple integration by substitution, follow these steps:
1. Identify the substitution variable, u.
2. Calculate the differential of u, du.
3. Rewrite the integral in terms of u.
4. Integrate the new integral.
5. Substitute back in the original variable, x.

4. What are some common substitution techniques used in simple integration?

Some common substitution techniques used in simple integration include:
1. u-substitution - replacing the variable with u = g(x).
2. Trigonometric substitution - replacing the variable with trigonometric functions such as sine, cosine, or tangent.
3. Exponential substitution - replacing the variable with exponential functions such as e^x.

5. Can I always use simple integration by substitution to solve an integral?

No, simple integration by substitution can only be used when there is a variable raised to a power that can be simplified by using a substitution. If the integral cannot be simplified in this way, other integration techniques may need to be used.

Similar threads

  • Calculus
Replies
6
Views
1K
Replies
8
Views
305
Replies
5
Views
1K
Replies
2
Views
1K
  • Calculus
Replies
2
Views
327
Replies
4
Views
2K
Replies
3
Views
1K
Replies
31
Views
749
  • Calculus
Replies
1
Views
963
Replies
10
Views
3K
Back
Top