Evaluate the Following Double Integral $\int _ { 0 } ^ { a } \int _ { 0 } ^ { \sqrt { e ^ { 2 } - x ^ { 2 } } } ( x + y ) d y d x$

question 180

Short Answer

Evaluate the following double integral: $\int _ { 0 } ^ { a } \int _ { 0 } ^ { \sqrt { e ^ { 2 } - x ^ { 2 } } } ( x + y ) d y d x$ , where a > 0.

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Definitions:

Contribution Margin

The amount remaining from sales revenue after variable costs are deducted, contributing to covering fixed costs and generating profit.

Break-Even Point

The financial point at which costs equal revenues, so there is no net loss or gain.

Contribution Margin

The amount remaining from sales revenue after variable expenses have been deducted, contributing to covering fixed costs and profit.

Break Even

is the point at which total costs and total revenues are equal, meaning there is no net loss or gain, and it's a rephrased term for determining financial balance.