anonymous
  • anonymous
evaluate the area of region bounded by the parabola x=y^2 and x=2y-y^2...
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
It's always when evaluating area of such regions to draw them. I don't like to use the draw feature, so I will try to solve it without drawing. First step you should do here is finding intersection points by setting the two parabolas equal, \[y^2=2y-y^2 \implies 2y^2-2y=0 \implies y=0 \text{ or y=1}.\] This tells us that the two curves will intersect at y=0 and y=1, and those will be the limit of the integral that will give us the area. The integrand should be the difference of the two curves, (the one with higher values inside the interval minus the one with the smaller values.) You can plug y=1/2, for example, to see that \(x=2y-y^2\) is greater inside \((0,1)\), thus the area is \(\large A=\int_0^1 (2y-y^2-y^2)dy \implies A=\int_0^1(2y-2y^2)dy.\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.