The Area of the Region That Lies to the Right $y$

question 106

Short Answer

The area of the region that lies to the right of the $y$ -axis and to the left of the parabola $x = 2 y - y ^ { 2 }$ (the shaded region in the figure) is given by the integral $\int _ { 0 } ^ { 2 } \left( 2 y - y ^ { 2 } \right) d y$ .
Find the area..

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Definitions:

Correlational Methods

Research techniques that study the relationship between two or more variables without determining cause and effect.

Experimental Methods

Research strategies involving the manipulation of one variable to determine its effect on another variable, within a controlled environment, to establish cause-and-effect relationships.

Randomly Assign

The process of distributing participants in a study into different groups using random methods to ensure that each participant has an equal chance of being assigned to any group.

Variable

A characteristic or quantity that can vary or change within a study, research, or mathematical model.