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**Anthony Lahmann****Member**- Registered: 2019-04-25
- Posts: 9

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,872

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

Children are not defined by school ...........The Fonz

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 Bundy

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Anthony Lahmann wrote:

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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**Anthony Lahmann****Member**- Registered: 2019-04-25
- Posts: 9

bob bundy wrote:

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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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,372

Anthony Lahmann wrote:

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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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 693
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bob bundy wrote:

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:

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[*]

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If you think the results are strange, remember the identity:

[list=*]

[*]

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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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