Integration/Area under Curve Problem help.

[rkltkdlee]

The Problem
Find the region bounded by the two functions from y=0 to y=2

equations given:
x=(y-1)² -1
x=(y-1)^{2 +1}



Attempt

1)Setting the equation against y.

sqrt(x+1) + 1 =y
sqrt(x-1 ) + 1 = y

Graphing

The Confusion

The second equation doesn't actually exist until x =1...does that mean I have to just integrate from 1 to 2? But....

It says from y=0 to y=2... I am confused about this. I am told to express x as a function of y and integrate it with respect to y.... I am unclear as to the meaning of this. It would make more sense if this was x=0 to x=2... please help!

 

[pappus]

The Problem
Find the region bounded by the two functions from y=0 to y=2

equations given:
x=(y-1)² -1
x=(y-1)<sup>2 +1

These equations describe parabolas opening to the right.</sup>

Attempt

1)Setting the equation against y.

sqrt(x+1) + 1 =y
sqrt(x-1 ) + 1 = y

Graphing

The Confusion

The second equation doesn't actually exist until x =1...does that mean I have to just integrate from 1 to 2? But....

It says from y=0 to y=2... I am confused about this. I am told to express x as a function of y and integrate it with respect to y.... I am unclear as to the meaning of this. It would make more sense if this was x=0 to x=2... please help!

1. Determine the vertices of the parabolas. Draw a sketch!

2. The parabolas and the two straight lines belong to the borders of an area. Calculate the area by integrating wrt y.