Consider the Integral $\int _ { 0 } ^ { 3 } \int _ { - x } ^ { 0 } f ( x , y ) d y d x$

question 12

Essay

Consider the integral $\int _ { 0 } ^ { 3 } \int _ { - x } ^ { 0 } f ( x , y ) d y d x$ .
(a)Sketch the region of integration and rewrite the integral with order of integration reversed.
(b)Rewrite the integral in polar coordinates.

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Definitions:

Incarceration Rates

The number of individuals within a population who are confined in prison or jail, expressed per 100,000 of the population.

Overrepresented

The state of being represented in a disproportionately high quantity relative to the actual population or occurrence rate.

Prison System

The organizational structure responsible for the detention, rehabilitation, and management of individuals convicted of crimes, encompassing various institutions and practices.

Ipperwash Crisis

A conflict in Canada between Indigenous people and the Ontario Provincial Police in 1995, centered around land claims and resulting in the death of an Indigenous protester.