Evaluate the Surface Integral $z ^ { 2 } + y ^ { 2 } = 1$

question 56

Short Answer

Evaluate the surface integral. S is the part of the cylinder $z ^ { 2 } + y ^ { 2 } = 1$ between the planes $x = 0$ and $x = 1$ in the first octant. $\iint _ { S } 4 \left( x ^ { 2 } y + z \right) d S$

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Definitions:

Net Profit

The financial gain or loss a business makes after subtracting all expenses, taxes, and costs from total revenue.

Shadow Price

In linear programming, it refers to the value that represents the change in the optimal objective function value per unit increase in the right-hand side of a constraint.

Finishing Constraint

A limitation or requirement in the production process that must be met before a product can be completed and delivered.

Total Profit

Total profit is the total income of a business after subtracting all expenses.