Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Integration

What am I doing wrong here?

Question

Given that f'(x) > 0 for a ≤ x ≤ b, and that g is the inverse of f, prove, by means of making a suitable change of variable:

where

My answer

Let

and let

But

Why am I out by a factor of 2?

Thanks

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Integration

I'm extremely rusty on this stuff, particularly integration by parts, so this is probably completely wrong.  However, it looks to me like the second term of your integration by parts is slightly off.  Instead of

shouldn't it be

Then you can split it into 2 integrals:

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Wrap it in bacon

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Integration

You're absolutely right, TheDude.

Thanks a lot.