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#1 2019-05-12 11:45:12
- Anthony Lahmann
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- Registered: 2019-04-25
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Integral of 1/sqrt(1-x^2)
How do you integrate
by u-substitution? Here's how I did it:After we did the u-substitution, we end up with the exact same integral, but with a negative in the front. What happened?
Last edited by Anthony Lahmann (2020-01-05 19:00:16)
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#2 2019-05-12 19:01:02
- Bob
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Re: Integral of 1/sqrt(1-x^2)
hi Anthony Lahmann
Welcome to the forum.
According to Wolfram Alpha, this is sin-1(x) and the second is -sin-1(x). So there's a sign error in there somewhere. I'll try to track it down later.
Bob
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You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2019-05-12 22:37:24
Re: Integral of 1/sqrt(1-x^2)
I will integrate 1/sqrt(1-x^2) by u-substitution. Here's how I did it:
After we did the u-substitution, we end up with the exact same integral, but with a negative in the front. What happened?
Your issue is here:
The correct implication is:
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#4 2019-05-13 12:23:15
- Anthony Lahmann
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- Registered: 2019-04-25
- Posts: 9
Re: Integral of 1/sqrt(1-x^2)
hi Anthony Lahmann
Welcome to the forum.
According to Wolfram Alpha, this is sin-1(x) and the second is -sin-1(x). So there's a sign error in there somewhere. I'll try to track it down later.
Bob
There is nothing wrong with this! I differentiated the u correctly, and I solved for x correctly.
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#5 2019-05-14 00:00:27
- George,Y
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Re: Integral of 1/sqrt(1-x^2)
There is nothing wrong with this! I differentiated the u correctly, and I solved for x correctly.
the last change of u to x is your mistake.
X'(y-Xβ)=0
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#6 2019-05-14 00:35:11
- Alg Num Theory
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Re: Integral of 1/sqrt(1-x^2)
According to Wolfram Alpha, this is sin-1(x) and the second is -sin-1(x).
Funny – I wonder why it didn’t give the second one as cos⁻¹(x).
If you integrate correctly, you should get:
[list=*]
[*]
[/list]
If you think the results are strange, remember the identity:
[list=*]
[*]
[/list]
Also when you integrate, do not forget to include an arbitrary constant.
Me, or the ugly man, whatever (3,3,6)
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