Question

5. Set S = {(x, y, z) € R³ | x² + y² + z² = a²}. Give an orientation and orientation preserving parametrization to S and calculate the following surface integral: \text { (i) } \iint_{S} d x \wedge d y+d y \wedge d z+d z \wedge d x \text {. } \text { (ii) } \iint_{S} z^{2} d x \wedge d y+x^{2} d y \wedge d z+y^{2} d z \wedge d x \text {. }

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