• Support PF! Buy your school textbooks, materials and every day products Here!

How the ? (Integration / Somewhat Urgent)

  • Thread starter Lunar Guy
  • Start date
  • #1
17
0
1. Integrate on the interval [0, 1]: (x2 - 1)/(x2 + 1)

2. No relevant equations.

3.

S x2/(x2 + 1) - [S 1/(x2 + 1)] =

S (x2 + 1) - 1/(x2 + 1) - [(arctan x)] =

S -1 - [(arctan x)] =

-x - arctan x

I can plug in the numbers on my own, but I would like to know if what I've done so far is correct...

Thanks to anyone who reads this and answers it.

- Lunar Guy
 
Last edited:

Answers and Replies

  • #2
1,013
65
How does ((x2 + 1) - 1)/(x2 + 1) become -1?
 
  • #3
a.a
127
0
the (x^2 + 1) cancles
but where did u get x2/(x2 + 1) from?
x^2 - 1 = x - 1)(x+1)
 
  • #4
1,013
65
the (x^2 + 1) cancles
but where did u get x2/(x2 + 1) from?
x^2 - 1 = x - 1)(x+1)
The (x2 + 1) cancels to become 1 - (1/(x2 + 1)), not -1.
He got x2/(x2 + 1) from (a + b)/c = a/c + b/c.
 
  • #5
a.a
127
0
so how does x^2/(x^2 +1) reduce to x^2 +1?
 
  • #6
1,013
65
so how does x^2/(x^2 +1) reduce to x^2 +1?
That never happened. He skipped the step x2 = x2 + 1 - 1.
 
  • #7
318
0
Think its quite easy... Convert the neumerator in the form of the denominator by writing -1 as 1-2
 
  • #8
318
0
So now you get (xsquare + 1) - 2
 

Related Threads for: How the ? (Integration / Somewhat Urgent)

  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
5
Views
1K
Replies
10
Views
2K
Replies
1
Views
367
Replies
2
Views
903
Top