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Integration Problem

I have to integrate using parts, but there is one step I don't understand, please can someone explain it?
When integrating sqrt(a^2-z^2) you get:
zsqrt(a^2-z^2) - integral(-z^2/(sqrt(a^2-z^2)))
which can then be split into:
zsqrt(a^2-z^2) - integral(a^2-z^2/(sqrt(a^2-z^2))) - integral(a^2/(sqrt(a^2-z^2)))

Now the next step is written:
integral 2sqrt(a^2-z^2)=zsqrt(a^2-z^2) - integral(a/(sqrt(1-(z/a)^2)))

I don't see how this was generated, as it doesn't seem like everything has been multiplied by 2 as it should have been done?
Did one of the integrals get moved to the other side?
a2z2a2z2=a2z2\displaystyle \frac{a^2-z^2}{\sqrt{a^2-z^2}} = \sqrt{a^2-z^2}
(edited 8 years ago)
Kindly write on paper and take a pic.

Same way you guys do on snapchat..lol

Let's see the problem clearly pls
Reply 3
Original post by EricPiphany
Did one of the integrals get moved to the other side?


Don't think so, they then go on to divide by 2 to get the original integral back :/
Original post by EricPiphany
Did one of the integrals get moved to the other side?
a2z2a2z2=a2z2\displaystyle \frac{a^2-z^2}{\sqrt{a^2-z^2}} = \sqrt{a^2-z^2}


Original post by EllieLC
Don't think so, they then go on to divide by 2 to get the original integral back :/


Try simplify as I've shown, and then move one of the integrals to the other side.
Reply 5
IMG_4566.jpg

That last step.. it then goes on to divide by 2 and do the last integral
Original post by EllieLC
IMG_4566.jpg

That last step.. it then goes on to divide by 2 and do the last integral

It is clear to me that you made some typos.

But to address your question, they collected like terms in the penultimate equation to get the last equation. Notice that the middle term in the penultimate equation is similar to the L.H.S.

Also, the last term was only simplified by multiplying the numerator and the denominator by 1/a each
(edited 8 years ago)
Original post by EllieLC
IMG_4566.jpg

That last step.. it then goes on to divide by 2 and do the last integral


You have a mistake in the second line: Plus a^2 and subtract a^2.
(edited 8 years ago)
Reply 8
Original post by Onlineslayer
It is clear to me that you made some typos.

But to address your question, they collected like terms in the penultimate equation to get the last equation. Notice that the middle term in the penultimate equation is similar to the L.H.S.

Also, the last term was only simplified by multiplying the numerator and the denominator by 1/a each


Ah I see, so the middle term in the penultimate equation was taken to the other side as suggested before!
Thank you very much, both :smile:
Reply 9
Original post by EricPiphany
You have a mistake in the second line: Plus a^2 and subtract a^2.


Original post by EllieLC
Ah I see, so the middle term in the penultimate equation was taken to the other side as suggested before!
Thank you very much, both :smile:


Original post by Onlineslayer
It is clear to me that you made some typos.

But to address your question, they collected like terms in the penultimate equation to get the last equation. Notice that the middle term in the penultimate equation is similar to the L.H.S.

Also, the last term was only simplified by multiplying the numerator and the denominator by 1/a each


http://www.thestudentroom.co.uk/showthread.php?t=819619


I'm on my phone, I don't even look where a thread is posted.

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