Answer:
Attached please find response.
Step-by-step explanation:
We wish to find the area between the curves 2x+y2=8 and y=x.
Substituting y for x in the equation 2x+y2=8 yields
2y+y2y2+2y−8(y+4)(y−2)=8=0=0
so the line y=x intersects the parabola 2x+y2=8 at the points (−4,−4) and (2,2). Solving the equation 2x+y2=8 for x yields
x=4−12y2
From sketching the graphs of the parabola and the line, we see that the x-values on the parabola are at least those on the line when −4≤y≤2.
In this exercise we have to use the function informed to identify the value of the formed figure, then:
[tex]x=4-12y^2[/tex]
Given the following information in the exercise statement:
Substituting y for x in the equation:
[tex]2y+y^2\\y^2+2y-8(y+4)(y-2)=8[/tex]
Analyzing the equation formed, we can see that it will have the shape of a parabola, and that the values of x will be between:
[tex]X: -4\leq y\leq 2[/tex]
See more about functions at brainly.com/question/5245372
