Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Integration

Hello

Does anyone mind checking my working? This turned out quite messy... have I missed something and overcomplicated it? Is there any better way to do it?

There is one line in particular I have a query about, and have marked it with a star (I guessed the latex code and got it right ) -  when I square root here, do I/how do I consider the negative root? EDIT: I'm guessing it doesn't matter? If I take ± on the outside of the integral it will just give me a ± answer, but as we are dealing with areas we can ignore the negative?

Thanks. I know it's longgg. Comfort yourself with the thought of how long it took me to type

Last edited by Daniel123 (2008-04-17 06:13:23)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Integration

I followed it all and learned a lot, but you are ahead of me on this so I can't critique.
But I think you are right about the plus or minus coming out of the integral after the star.
And perhaps since the limits of integration are all in 1st quadrant, then
maybe that allows you to do the plus/minus thing.
If the limits went several times around a circle, then I can see that
you could get differing areas, because the square root could potentially
be a negative absolute value of a cosine wave, which would accumulate
negative area as you integrate area to the right, if this always negative
wave never went above the x-axis.

I knew some Calculus in the 1980's.

Last edited by John E. Franklin (2008-04-09 09:05:47)

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igloo myrtilles fourmis

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Integration

Yes you dont need to worry about the negative root.

Trigonometric substitution. I checked all your work and its correct.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Integration

Great, thanks Luis and John.