Evaluate the Integral $\int _ { 0 } ^ { 2 } \int _ { - \sqrt { 2 y - y ^ { 2 } } } ^ { \sqrt { 2 y - y ^ { 2 } } } y d x d y$

question 115

Short Answer

Evaluate the integral $\int _ { 0 } ^ { 2 } \int _ { - \sqrt { 2 y - y ^ { 2 } } } ^ { \sqrt { 2 y - y ^ { 2 } } } y d x d y$ by changing to polar coordinates.

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Definitions:

Periodic Inventory

An inventory accounting system where the inventory is updated and the cost of goods sold is calculated at the end of a period instead of after each sale.

Inventory Balance

Refers to the total value of all inventory a business has in stock at a specific point in time, including raw materials, work-in-progress, and finished goods.

Replacement Cost

The amount required to replace an asset at current prices, ensuring similar functionality or capacity.

Inventory Turnover

A measure of how many times a company's inventory is sold and replaced over a certain period, indicating the efficiency of inventory management.