Evaluate the Integral $\iint _ { R } \frac { x ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } d A$

question 75

Short Answer

Evaluate the integral $\iint _ { R } \frac { x ^ { 2 } } { x ^ { 2 } + y ^ { 2 } } d A$ , where $R$ is the annular region bounded by the circles $x ^ { 2 } + y ^ { 2 } = 9$ and $x ^ { 2 } + y ^ { 2 } = 16$ , by changing to polar coordinates.

---

Definitions:

Marginal Utility

The additional satisfaction gained from consuming one more unit of a good or service.

Market Basket

A set of goods and services used to represent what is consumed by a typical consumer for the purpose of measuring inflation or cost of living.

Utility Maximization

The process by which individuals allocate their resources to obtain the highest possible level of satisfaction or utility, subject to their budget constraint.

Marginal Utility

The change in total utility obtained by consuming one additional unit of a good or service.