A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 4 years ago

evaluate the area of region bounded by the parabola x=y^2 and x=2y-y^2...

  • This Question is Closed
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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 \(\large A=\int_0^1 (2y-y^2-y^2)dy \implies A=\int_0^1(2y-2y^2)dy.\)

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.