Finding Area Between x=2(y^2) & x+y=1

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SUMMARY

The discussion centers on finding the area between the curves defined by the equations x=2(y^2) and x+y=1. The user initially attempted to find the intersection points by solving the equation 2(y^2)=1-y, resulting in y=0 and y=1. However, a different method employed by the teacher, which involved solving the quadratic equation 2(y^2)+y-1=0, yielded intersection points of y=-1 and y=1/2. This discrepancy raised questions about the validity of both methods and their results.

PREREQUISITES
  • Understanding of quadratic equations and their solutions
  • Knowledge of curve intersections in coordinate geometry
  • Familiarity with the concept of area between curves
  • Basic algebraic manipulation skills
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  • Learn how to find intersection points of curves graphically and algebraically
  • Explore the process of calculating the area between two curves using definite integrals
  • Review examples of similar problems involving area calculations between different types of functions
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Students studying calculus, particularly those focusing on area calculations between curves, as well as educators looking to clarify methods for solving intersection problems in algebra and geometry.

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Homework Statement


Find the area between
x=2(y^2) and x+y=1



The Attempt at a Solution


First I'm trying to find their intersection so

To solve for y I set up:
2(y^2)=1-y
2(y^2)+y=1
y=0,1

But, I notice that my teacher did:
2(y^2)+y-1=0
(2y+1)(y-1)=0
y=-1, 1/2

Why are these 2 methods bringing about different answers? Shouldn't they be the same?
 
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