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Basically I want to know if the formulas I arrive for the flux of a Toroid and a Solenoid are correct

Leaving aside the integration part this is the basic formula for the flux

[itex]\phi = BNA[/itex]

B = magnetic field

N = number of turns of the solenoid/toroid

A = Area

So for the solenoid I arrive to this:

[itex]B = \mu nI[/itex] -> n = N/L

[itex]A = 2\pi r(r+l)[/itex] this is the area for a cylinder

[itex]\phi = \mu nINA = \frac{\mu IN^{2}}{L}2\pi r(r+L)[/itex]

For the toroid I arrive to this:

[itex]B = \frac{\mu NI}{2\pi r}[/itex]

[itex]\phi = \int BNdr = \frac{\mu IN^{2}}{2\pi}ln\frac{b}{a} [/itex]