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Let $C$ be the intersection of sphere:

$$x^2+y^2+z^2=a^2$$

...and plane:

$$x+z=a$$$$a>0$$

...is a constant. Calculate the line integral:

$$I=\int_C y^2 ds$$

$\cfrac{a^3\pi}{2\sqrt{2}}$

$\cfrac{a^2\pi}{2}$

$\cfrac{\pi}{2\sqrt{2}}$

$\pi a^2$

$\sqrt{2}\pi$