Compute $\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A }$

question 3

Short Answer

Compute $\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A }$ , where S is oriented in the positive $\vec { j }$ direction and given, for 0 $\le$ s $\le$ 1, 0 $\le$ t $\le$ 2, by x = s, y = t², z =8 t.

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Definitions:

Germany

A country in Central Europe known for its rich history, economic strength, and contributions to arts, science, and technology.

France

A country in Western Europe known for its rich history, culture, and significant impact on global politics, cuisine, and the arts.

Market Failure

An instance where a laissez-faire market's distribution of goods and services is inefficient, typically resulting in a reduction of collective social welfare.

Centrally Planned Economy

An economic system where the government makes all decisions on the production and consumption of goods and services.