Using Divergence Theorem to evaluate the flux over a sphere

Question

Above is the question. I've try to find the divergence of F and parameterize the sphere using spherical coordinates. Below is my work. Then I use online integral calculator(just to avoid human error) to find the result is $100000\pi/3$, but the result isn't right. Is anything wrong with my work? I don't think it is calculation mistake since I calculate it using computer...Can anyone help please?

Answer 1

when doing the conversion to spherical polars you should not use $\sqrt 2$ for $p$

so $$I=4I_1I_2I_3$$

and $$I_1 =\int_0^\sqrt 2 p^6 dp = \frac 17 (\sqrt2)^7 = \frac{8 \sqrt 2}{7} $$

So $$ I = \frac{128 \sqrt 2 \pi}{35} $$

Answer 2

$$ I_1= \int _0^\sqrt2 p^2 dp =\frac 13(\sqrt2)^3 = \frac{2\sqrt 2}{3} $$

$$ I_2= \int _0^{2\pi }d\theta = 2\pi $$

$$ I_3 = \int _0^{\pi }cos^4\phi \sin\phi d\phi = -\int_1^{-1}u^4 du=\frac 25$$

So

$$ I = 16 I_1I_2I_3 = \frac{128\sqrt2 \pi}{15} $$