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October 27th, 2010, 06:15 PM   #1
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Integration

Hi,

I require help with this problem. I'm asking kindly for help. Hints...

.
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October 27th, 2010, 07:29 PM   #2
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Re: Integration

Quote:
Originally Posted by MathematicallyObtuse
Hi,

I require help with this problem. I'm asking kindly for help. Hints...

.












Therefor....



So,

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October 27th, 2010, 07:51 PM   #3
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Re: Integration

We have:



A definite integral can be evaluated using integration by parts in the following manner:



We will let and , thus

and

Putting it together, we have:



The expression to the left of the integral is zero, and using the Pythagorean identity for , we have:



Solve for







Thus,

edit: Sorry, stainburg, I didn't catch that you had already solved.
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October 27th, 2010, 07:55 PM   #4
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Re: Integration

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Originally Posted by MarkFL
edit: Sorry, stainburg, I didn't catch that you had already solved.
Urh...haven't you ever slept? You are always online.
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October 27th, 2010, 08:04 PM   #5
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Re: Integration

I require very little sleep.
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October 27th, 2010, 08:15 PM   #6
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Re: Integration

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I require very little sleep.
You should take some physical exercise to help sleep
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November 2nd, 2010, 07:06 PM   #7
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Re: Integration

Thanks.

The next part may or not be a follow-up to the question. I worked it out. I just think it's unnecessarily tedious.
Hmmm...ponders





Then for the definite integral:


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November 2nd, 2010, 07:42 PM   #8
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Re: Integration

You obtained the correct result (according to my TI-89) and in a much more elegant form. As a minor aside, you don't write the constant C after the result from a definite integral...it essentially gets subtracted away when you apply the F(b) - F(a) part of the anti-derivative form of the fundamental theorem of calculus...i.e.

[F(b) + C] - [F(a) + C] = F(b) - F(a)
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November 3rd, 2010, 01:26 AM   #9
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Re: Integration

Quote:
Originally Posted by MarkFL
You obtained the correct result (according to my TI-89) and in a much more elegant form. As a minor aside, you don't write the constant C after the result from a definite integral...it essentially gets subtracted away when you apply the F(b) - F(a) part of the anti-derivative form of the fundamental theorem of calculus...i.e.

[F(b) + C] - [F(a) + C] = F(b) - F(a)
Thanks.
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