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.
