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July 14th, 2017, 07:29 AM   #1
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split multiplication in integral

Hi, I've got an equation that looks like this:
$\displaystyle
G = \int_0^X 4\pi (g-1) r^2 \left( 1-\frac{3r}{4R} + \frac{3r^3}{16R^3} \right) dr
$

Now I would like to separate this integral into
$\displaystyle G = \int_0^X 4\pi (g-1) r^2 dr + Y $
or
$\displaystyle G = \int_0^X 4\pi (g-1) r^2 dr * Y $
where Y does not contain g.
Is this possible?

Last edited by skipjack; July 14th, 2017 at 10:03 AM.
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July 14th, 2017, 10:08 AM   #2
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Quote:
Originally Posted by Fadabi View Post
Hi, I've got an equation that looks like this:
$\displaystyle
G = \int_0^X 4\pi (g-1) r^2 \left( 1-\frac{3r}{4R} + \frac{3r^3}{16R^3} \right) dr
$

Now I would like to separate this integral into
$\displaystyle G = \int_0^X 4\pi (g-1) r^2 dr + Y $
or
$\displaystyle G = \int_0^X 4\pi (g-1) r^2 dr * Y $
where Y does not contain g.
Is this possible?
why not just complete the integral, it's not hard

$\displaystyle
G = \int_0^X 4\pi (g-1) r^2 \left( 1-\frac{3r}{4R} + \frac{3r^3}{16R^3} \right) dr =\dfrac{\pi (g-1) X^3 \left(32 R^3-18 R^2 X+3 X^3\right)}{24 R^3}
$
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July 14th, 2017, 01:08 PM   #3
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Does g depend on r? If not, direct integration (romsek) works. If g depends on r, what you want is unlikely.
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