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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }

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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } where F(x,y,z)=y2i+xj+zk\mathbf { F } ( x , y , z ) = y ^ { 2 } \mathbf { i } + x \mathbf { j } + z \mathbf { k } and S is the part of the surface z=x+y2z = x + y ^ { 2 } that lies above the rectangle (0x1,0y2)( 0 \leq x \leq 1,0 \leq y \leq 2 ) and has upward orientation.

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Definitions:

Defense Mechanisms

Subconscious practices engaged to block anxiety resulting from emotions or thoughts perceived as unacceptable.

Anxiety

An emotion characterized by apprehension or distress over an unpredictable result.

Countertransference

Emotional reactions of therapists toward their patients, often based on the therapist's own background and psychological issues.

Transference

A psychoanalytical concept where patients project feelings about figures from their past onto the therapist, unknowingly replicating past relationships.

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