Find the area bounded by the curves y2 = 2x + 6 and x = y + 1. your work must include an integral in one variable.

18.

Step-by-step explanation:

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.

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step-by-step explanation:

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step-by-step explanation:

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