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Calculate the integral:

$$I=\int_0^2 \int_0^2 \sqrt{u+v} dudv$$

A

$\cfrac{15(4-\sqrt{2})}{32}$

B

$\cfrac{32(4-\sqrt{2})}{15}$

C

$\cfrac{4(4-\sqrt{2})}{3}$

D

$\cfrac{8(5-2\sqrt{3})}{3}$

E

None of the above

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