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Multivariable Calculus

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Difficult

Scalar Line Integral using Elliptic Cylindrical Coordinates

MVCALC-L4M5AJ

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:

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

A

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

B

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

C

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

D

$\pi a^2$

E

$\sqrt{2}\pi$