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Multivariable Calculus

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Difficult

Scalar Line Integral on Tilted Circle

MVCALC-ECNU4E

Let $C$ be the intersection line of sphere:

$$x^2+y^2+z^2=1$$

...and plane:

$$x+y+z=0$$

Evaluate the line integral:

$$\oint_C (x-y+z^2) ds$$

A

$0$

B

$1$

C

$\cfrac{2\pi}{3}$

D

$\pi^2$

E

$\ln 2$