Question

100 POINTS

Find the area bounded by the curves x = 2y2 and x = 1 – y. Your work must include an integral in one variable.

Answer 1

i think its 18.

Explanation:

Answer 2

y^2 = 2x + 6

2x = y^2 - 6

x = 1/2(y^2 - 6)

The points of intersection of the curves are calculated:

y + 1 = 1/2( y^2 - 6)

2y + 2 = y^2 - 6

y^2 - 2y - 8 = 0

( y - 4)(y + 2) = 0

y = 4, -2

when y = 4, x = 5 and when y = -2 x = -1.

Integrating between y = 4 and y = -2

4

INT [ ( y + 1 + 1/2 (6 - y^2) ]dy

-2

= 4

{ y^2 / 2 + y + 3y - y^3/6 }

-2

= 13 1/3 - (-4 2/3)

13 1/3 + 4 2/3

= 18 answer.